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- July 15, 1997 -
- O P - S F N E T Volume 4, Number 4 -
- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -
- Editors: -
- Tom H. Koornwinder thk@wins.uva.nl -
- Martin Muldoon muldoon@yorku.ca -
- -
- The Electronic News Net of the SIAM Activity Group -
- on Orthogonal Polynomials and Special Functions -
- -
- Please send contributions to: poly@siam.org -
- & address changes to: poly-request@siam.org -
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Today's Topics:
1. Charter Renewal
2. Revising the 1991 Math. Subject Classification
3. Response from Math. Reviews
4. Bibliography on orthogonal polynomials (Keith Dennis)
5. Response from Tom Koornwinder
6. Editorial policy of SIAM Journal on Mathematical Analysis
7. Back issues of OP-SF Net
8. An OP-SF listserv?
9. Minisymposium on Handbooks of Special Functions (update)
10. Amsterdam Seminar on Special Functions and Group Theory
11. Call for Papers "Orthogonal Polynomials and Computer Algebra"
12. Maple and REDUCE Packages on q-Hypergeometric Summation
13. Project at Leuven on integral transformations
14. Positions at Kyushu University
15. Russian Newsletter on Integral Transforms and Special Functions
16. New Book Series
17. Book on Umbral Calculus
18. New Journal: Inequalities and Applications
19. Books on Special Functions in Astrophysics and Cosmology
20. Review of Gradshteyn and Ryzhik (book and CD-ROM)
21. Report on VI International Krawtchouk Conference (Kiev)
22. Report on Madison Centennial Conference
23. ftp site for papers in Orthogonal Polynomials and Special
Functions
24. Changes of Address, WWW Pages, etc.
25. Obtaining back issues of OP-SF Net and submitting contributions
to OP-SF Net and Newsletter
Calendar of events: see issue/topic:
1997
July 14-18: SIAM 45th Anniversary Meeting, Stanford, California
including Minisymposium on "Handbooks for Special Functions
and the World Wide Web" 4.2 #1. 4.4 #9
July 14-18: 9th International Conference on Formal Power Series
and Algebraic Combinatorics, Vienna, Austria 3.4 #7
July 28 - August 2: VIII International Conference on Symmetry
Methods in Physics, Dubna, Russia 4.2 #3
September 4: Seminar Special Functions and Group Theory, Amsterdam 4.4 #10
September 22-26: VIII Simposium sobre Polinomios Ortogonales y
Aplicaciones, Sevilla, Spain 3.5 #5, 4.2 #4 and 4.3 #5
1998
March 22-28: Meeting on Applications and Computation of Orthogonal
Polynomials, Oberwolfach, Germany 4.3 #6
July 13-17: SIAM Annual Meeting, Toronto, Canada
Topic #1 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Charles Dunkl
Subject: Charter Renewal
Dear Colleagues,
On June 12, 1997 I sent the followong document to Allison Bogardo at SIAM.
Charles Dunkl
CHARTER RENEWAL APPLICATION
This CHARTER RENEWAL APPLICATION (hereinafter called "RENEWAL") applies to
the SIAM Activity Group on Orthogonal Polynomials and Special Functions.
The SIAM Activity Group (hereinafter called "SIAG") to which this RENEWAL
applies was originally formed under the aegis of the Society for
Industrial and Applied Mathematics (hereinafter called "SIAM") in July 15,
1990 by the SIAM Council and July 19, 1990 by the SIAM Board of Trustees
with its initial operating period beginning Jan. 1, 1990 and ending Dec.
31, 1992. Its charter has been renewed by the council and board two times
thereafter. This SIAG has 133 members as of March 15, 1997.
According to its Rules of Procedure, the objectives of the SIAG are to
promote basic research in orthogonal polynomials and special functions; to
further the application of this subject in other parts of mathematics, and
in science and industry; and to encourage and support the exchange of
information, ideas and techniques between workers in this field, and other
mathematicians and scientists.
It's proposed functions are as follows:
"The group is concerned with the following topics and their
applications: general systems of orthogonal polynomials - asymptotic
analysis, three-term recurrence relations and Markov processes,
numerical quadrature, Julia sets, least-squares of orthogonal
polynomials - harmonic analysis, approximation theory, representations
of compact groups, quantum mechanics, combinatorics, coding and design
theory; orthogoanl polynomials in several variables - Lie groups,
tomography, optics, wave functions in crystals; special functions - for
example, Bessel, gamma, theta, spheroidal wave, etc., solutions of
partial differential equations, harmonic analysis of noncompact groups,
statistical mechanics, integral transforms, number theory.
"Activities will include dissemination of information about upcoming
conferences and sponsoring special sessions at SIAM meetings. Also,
the group will assist researchers in the use of symbolic computer
calculations by publicizing available software for special functions.
Another goal is to establish some working relationships with the
various SIAM journals, especially the one on mathematical analysis,
with the view of sporadically sponsoring some invited or contributed
articles."
It has complemented SIAM's activities and supported its proposed functions
as follows: The SIAG has sponsored a minisymposium at each of the recent
annual SIAM meetings. There is a printed newsletter which has three issues
annually. The electronic news service OP-SF Net is produced about six
times per year. There is an ftp site for electronic circulation of
preprints which is maintained by one of the SIAG's members, and it is
linked to the SIAG's permanent web site. The SIAG has been involved in
disseninating news about current projects of several groups of workers who
are planning handbooks of special functions, in print or digital forms.
These handbooks are intended to be used by the general mathematical and
scientific public. The vice chair of the SIAG has had discussions with a
new mathematical society dedicated to special functions, based in India,
regarding possible cooperation and links.
In an effort to continue to foster activities and interaction between
members of this group and the special functions community in general, this
SIAG has planned and proposes the following activities: There will be a
minisymposium at the July 1997 meeting in Stanford regarding the handbook
projects. There will be speakers representing the NIST project revising
the well-known Abramovitz and Stegun tables and the "Askey-Bateman"
project, which is taking the Erdelyi-Bateman "Higher Transcendental
Functions" series as its beginning point. These are both exciting projects
which should lead to much more useful ways of retrieving information about
and using special functions. One will be able to compute both symbolically
and numerically, locate references, and find useful facts. The newsletters
will continue to serve researchers and users of special functions, with
useful news about conferences, book and software reviews, and pointers to
the existing literature for the non-specialists. This list of instructive
survey articles and texts is a new feature of the print newsletter and has
been well received.
This SIAG requests that the SIAM Council and Board of Trustees renew its
charter for a three-year operating period beginning Jan. 1, 1999.
Topic #2 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Tom Koornwinder
Subject: Revising the 1991 Math. Subject Classification
The following message was sent on June 19, 1997 to Prof. Keith Dennis
(Executive Editor Mathematical Reviews) and Prof. Bernd Wegner
(Chefredakteur, Zentralblatt fuer Mathematik).
Dear Editors,
In reply to your call for comments and suggestions for the revision of the
Mathematics Subject Classification I send you here a large number of
suggestions from the community of Orthogonal Polynomials and Special
Functions. The SIAM Activity Group on Orthogonal Polynomials and Special
Functions has solicited reactions via the electronic Newsletter OP-SF Net
(freely available for all interested people) and the printed Newsletter of
the Activity Group (only for members). On the basis of the reactions we
received I have made a comprehensive proposal for changes of those parts
of the 1991 Classification which deal with Orthogonal Polynomials and
Special Functions (in particular part 33). A preliminary version of this
final proposal I recently discussed with prof. Richard Askey, and he
agreed with it.
Experts from our Activity Group are available if you need further
feed-back in the area of Orthogonal Polynomials and Special Functions
during your revision process.
With kind regards,
Tom Koornwinder
-----------------------
about 33
- 33C45, change into:
Orthogonal polynomials and functions of hypergeometric type
(Jacobi, Laguerre, Hermite, Askey scheme, etc.; see 42C05 for general
orthogonal polynomials and functions)
- add: 33C47 Other special orthogonal polynomials and functions
- 33C50: change into:
Orthogonal polynomials and functions in several variables expressible
in terms of special functions in one variable
- add: 33C52 Orthogonal polynomials and functions associated with root
systems
- 33C55, change into: Spherical harmonics
Motivation: ultraspherical polynomials unrelated to spherical harmonics
are covered by 33C45; spherical functions (on Gelfand pairs) are covered
by 33C80
- add: 33C67 Hypergeometric functions associated with root systems
- 33C80, change into: Connections with groups, algebras and related topics
- 33D10: skip this
Motivation: we know theta functions but we do not know basic theta
functions
- 33D15, change into:
Basic hypergeometric functions in one variable, ${}_r\phi_s$
- 33D20: skip this
Motivation: studying ${}_2\phi_1$ immediately gives rise to
studying more general ${}_r\phi_s$
- 33D45, change into: Basic orthogonal polynomials and functions
(Askey-Wilson polynomials, etc.)
- add: 33D50 Orthogonal polynomials and functions in several variables
expressible in terms of basic hypergeometric functions in one variable
- add: 33D52 Basic orthogonal polynomials and functions associated with
root systems (Macdonald polynomials, etc.)
- 33D55: skip this
Motivation: Basic spherical functions in the sense of spherical
functions on quantum groups are covered by 33D80. If basic spherical
harmonics mean the elements in irreducible subspaces of the algebra of
polynomials on a quantum sphere then these are also covered by 33D80.
- add: 33D67 Basic hypergeometric functions associated with root systems
- 33D80, change into: Connections with quantum groups, Chevalley groups,
p-adic groups, Hecke algebras and related topics
- add: 33E12 Mittag-Leffler functions and generalizations
- add: 33Fxx Computational aspects
- add: 33F05 Numerical approximation [See also 65D20]
- add: 33F10 Symbolic computation (Zeilberger algorithm, etc.)
[See also 68Q40]
about 34
- 34B30, change into:
Special equations (Mathieu, Hill, Bessel, Painlev\'e, etc.)
about 40
- add: 40A27 Explicit summation of series
- add: 40A29 Explicit computation of integrals
- add: 40A40 Generating functions [See also 05A15]
- add: 40B10 Rearrangements of explicit multiple series
- add: 40B15 Multiple integrals (should also be assigned at least one
other classification number in this section)
about 42
- 42C05, change into: Orthogonal functions and polynomials in one
variable, general theory [See also 33C45, 33C47, 33D45]
- add: 42C07 Orthogonal functions and polynomials in several variables,
general theory [See also 33C50, 33C52, 33D50, 33D52]
- add: 42C40 Wavelets
- add: 42C45 Biorthogonal families of functions
- 65D20, change into: Computation of special functions, construction of
tables [See also 33F05]
about 68
- 68Q40, add to "See also" a ref to 33F10
(warning: 68Q40 gives a ref to 16-08, but 16-08 does not exist)
Topic #3 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Patrick Ion
Subject: Re: Revising the 1991 Math. Subject Classification
Dear Professor Koornwinder,
Thank you very much for the carefully considered suggestions for revision
of the MSC you have sent from the OP-SF group. You have clearly not only
tried to improve the scientific quality of the scheme, but also been
mindful of the technical constraints that we at MR and Zbl work under in
revising something long used for database access.
Speaking only directly in connection with the area 33 (Special Functions)
which I am myself involved with editorially, I can say that I hope we
shall be able to adopt almost all your suggestions. I would like to take
a later opportunity to respond to some of your proposals, and to provoke
more expert input to our revision process.
Thank you again for your, and your group's, willingness to help with
MSC2000.
Best regards,
Patrick Ion
Associate Editor
Mathematical Reviews
P. O. Box 8604
Ann Arbor, MI 48107-8604
Topic #4 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Keith Dennis
Subject: Bibliography on orthogonal polynomials
Editor's note:
In OP-SF Net 3,6, Topic #10, Dick Askey wrote about the Bibliography on
Orthogonal Polynomials published in 1940 by Shohat, Hille and Walsh.
Professor Keith Dennis, managing editor of Math. Reviews, has proposed
preparing an electronic version of this bibliography. We quote the
following from a message he sent us last January.
Let me clarify a bit how I was proposing that Mathematical Reviews be
involved in the project. First of all I should say that from my point
of view the main goal is to get as much bibliographic information as
possible into a reasonably standard format. Ideally this would mean
1. placing the data in appropriate fields (author, title, journal,
volume, year, etc.);
2. identifying the journal or series;
3. identifing the author;
4. classifying the information using a uniform scheme;
5. providing a review or abstract of the article.
In the case of the Shohat bibliography I think that the detailed
classification given there could be used to create a sort of
combination of 4 & 5.
This is not exactly the same format as that for current MR data, but
it is about as close as one can get without a lot of additional
effort.
My original intent was that Mathematical Reviews, with support from the
mathematical community, would carry out the details of putting the data in
an appropriate form. That is, from the point of view of putting the
existing bibliography into usable form, no additional person would be
necessary to direct the project. However, if one wanted to update this,
or integrate it with current MR or Zbl, or if one wanted to assign current
MSC classifications, then extra help would certainly be necessary.
My original estimate of $5000 would be to carry out most of the project:
The book is 200 pages long but with very intricate classifications that
would have to be carefully proofread. The actual keyboarding &
proofreading can no doubt be done for quite a bit less. However, I wanted
to include the extra work to identify the journals & individuals (as they
are already grouped this way, this would mean merging with the MR
individual database) and writing scripts to derive a written description
of the classification for each item.
I was further proposing that MR take whatever steps necessary to deal with
any copyright problems.
We have experience with a number of keyboarding companies (e.g., the
reviews from 1940 through 1979 are currently in the process of being
converted to text form) and this might well be the cheapest input method.
However, due to the fine detail in the classification, I believe that we
will also want to have it proofread again, but fortunately it is only 200
pages long.
So what I was proposing was that community raise the necessary funds for
the data entry as described above.
..........
I would propose that we attempt to start with a smaller project,
converting the Shohat bibliography into electronic form. Then if this
raises sufficient interest in the community, perhaps an editorial group
could be put together to update it in a useful way.
Topic #5 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Tom Koornwinder
Subject: Re: Bibliography on orthogonal polynomials
The officers of our Activity Group have discussed the plans of Keith
Dennis for an elctronic update of the Shohat bibliography on orthogonal
polynomials (see topic above). Our conclusion is that we are sympathetic
concerning these proposals, but that we do not see it as a top priority
for our group. We feel that providing bibliographic information of recent
work on OP & SF (cf. for instance the Compiled Booklist in OP-SF Net 4.2,
Topic #12) should have a higher priority for us. Therefore we have
written to Prof. Dennis that our Activity Group will not contribute
financially to his project. Of course, this leaves open the possibility
for individual members, that they may contribute.
Topic #6 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Tom Koornwinder
Subject: Editorial policy of SIAM Journal on Mathematical Analysis
The following is endorsed by all officers of our Activity Group.
Traditionally, SIAM Journal on Mathematical Analysis has been closest of
all SIAM journals to the scientific purposes of our Activity Group. From
the start of this journal in the early seventies onward, many papers on OP
& SF have appeared in SIAM J. Math. Anal. including some of the best
papers in our area. A typical example is Ian Macdonald's paper "Some
conjectures for root systems" in Vol. 13 (1982), pp. 988-1007, which has
had an enormous impact.
The editorial policy of SIAM J. Math. Analysis is given by the following
lines (see http://www.siam.org/journals/sima/mapol.htm):
"The SIAM Journal on Mathematical Analysis focuses on those parts of
classical and modern analysis that have direct or potential application to
the natural sciences and engineering. Papers fall into two broad
categories, the first being those that analyze interesting problems
associated with realistic mathematical models for natural phenomena. The
second category includes those papers which contribute in a substantial
way to the general, analytical information and techniques which are likely
to bear upon such models."
Implementation of this policy has become more strict. This can be seen
from:
- inspection of the tables of contents
- recent experiences that papers on OP & SF of a more theoretical nature
were rejected as a matter of policy rather than because of the quality
of the contributions
- Charles Dunkl having quit from the Editorial board and not being
succeeded by a specialist in theoretical aspects of OP & SF.
We are aware that our Activity Group, more than the other Activity Groups
in SIAM, houses members whose research is motivated by theory rather than
by application. Still, the potential of applications (in one, ten or fifty
years) is an important aspect of OP & SF. Anyhow, for an Activity Group
within SIAM, it is unfortunate if an important part of the membership
cannot publish in any SIAM journal.
According to Nico Temme, who is at present a member of the Editorial Board
of SIAM J. Math. Anal., there is a good chance that a theoretical paper
with enough mathematical quality and novelty will improve its suitability
for SIAM J. Math. Anal. if the author takes a few sentences or paragraphs
to address the possibility of specific applications, with a few examples.
We would suggest our readers to keep trying to submit papers (keeping
Nico's advise in mind), but to report to us (the officers of the Activity
Group) if your paper is rejected just because it is out of scope. Such
reports will be collected by Tom Koornwinder . We will be
able to read about positive experiences in the list of accepted papers
(http://www.siam.org/journals/sima/maarts.htm).
In about one year we intend to write an evaluation in OP-SF Net.
Topic #7 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Tom Koornwinder
Subject: Back issues of OP-SF Net
>From now on, back issues of OP-SF Net can also be obtained from the URL:
http://turing.wins.uva.nl/~thk/opsfnet/
with a more convenient interface. The possibility to download by ftp from:
ftp.wins.uva.nl, in directory
pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir
will remain.
Topic #8 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Editor
Subject: An OP-SF listserv?
It has been suggested that an OPSF listserv should be started. None such
exist now to my knowledge. I believe it would not be difficult to have one
set up at some university with an address of the form OPSF-L@... . Such a
listserv could be useful in promoting discussion and posing questions in
the general areas of orthogonal polynomials and special functions. A
selection of contributions could be included in OP-SF NET. It has been
suggested that we might create an automatic way to subscribe and
unsubscribe to the listserv and OP-SF NET. To make it workable, the
listserv would probably have to be "unmoderated" which means that the
Group would have no control over what might appear there. Some have
observed that this could lead to abuse. In any case, such a listserv
need not have any official connection to our Activity Group, though it
could be publicized in the Group's media. Of course if it used the
acronym OPSF it would be associated with the Group, in people's minds, in
any case. Let me know what you think of the idea of starting such a
listserv; your comments can be sent to muldoon@yorku.ca. If it seems to be
a good idea, would anyone like to volunteer to set it up?
Topic #9 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Willard Miller
Subject: Minisymposium on Handbooks of Special Functions
The program of the Minisymposium on "Handbooks for Special Functions and
the World Wide Web" (see OP-SF NET 4.2, #1) scheduled for Monday, July 14
at the SIAM Annual Meeting at Stanford University has been modified by the
addition of a talk on the Mathematica Interactive Special Functions
Handbook Project. The description of the talk is as follows:
Speakers: O.I. Marichev, P. Wellin
Wolfram Research, oleg@wolfram.com
Contributors: V.S. Adamchik, M. Trott, S. Wolfram, R. Germundsson,
A. Kuzniarek, J. Novak, N. Soiffer, M. Sofroniou
Title: The Mathematica Interactive Special Functions Handbook Project
A team of experts in special functions, numerical analysis,
programming languages, and interface design at Wolfram Research have
been developing tools to produce electronic, interactive versions of
the math and science handbooks using the recently released Mathematica
Version 3.0. In this talk, we will present current work on the Special
Functions Handbook giving an overview of the project, as well as
specific examples that will demonstrate solutions to issues of formula
representation, presentation and navigation, formula searching, and
distribution.
Topic #10 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Erik Koelink
Subject: Seminar SPECIAL FUNCTIONS and GROUP THEORY, Amsterdam
Program
11:00-12.00 Sander Hille (Rijksuniversiteit Leiden)
Canonical representations of SU(1,n) associated to a character
12.15-13.15 Joris Van der Jeugt (Universiteit Gent, Belgium)
Representation theory and orthogonal polynomials: convolution
formulas and bilinear generating functions
14.30-15.30 Hjalmar Rosengren (Lunds Universitet, Sweden)
Coupling coefficients and multivariable orthogonal polynomials
16.00-17.00 Tom Koornwinder (Universiteit van Amsterdam)
The A1 tableau of Dunkl-Cherednik operators
Date: Thursday, September 4, 1997.
Place: Department of Mathematics, University of Amsterdam,
Plantage Muidergracht 24, 1018 TV Amsterdam.
See http://turing.wins.uva.nl/~koelink/semSFGT.html
Contact: Erik Koelink, koelink@wins.uva.nl
Topic #11 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Wolfram Koepf
Subject: Call for Papers "Orthogonal Polynomials and Computer Algebra".
Journal of Symbolic Computation
Special Issue on Orthogonal Polynomials and Computer Algebra
R. A. Askey, W. Koepf and T. H. Koornwinder, guest editors
In the last decade major steps towards an algorithmic treatment of
orthogonal polynomials and special functions (OP & SF) have been made,
notably Zeilberger's brilliant extension of Gosper's algorithm on
algorithmic definite hypergeometric summation. By implementations of these
and other algorithms symbolic computation has the potential to change the
daily work of everybody who uses orthogonal polynomials or special
functions in research or applications. It can be expected that symbolic
computation will also play an important role in on-line versions of major
revisions of existing formula books in the area of OP & SF.
Many articles on the algorithmic treatment of orthogonal polynomials and
special functions and on applications of such algorithms have been
published in the meantime. But such articles are distributed widely in the
literature. To collect these efforts Wolfram Koepf organized Session 13 on
Orthogonal Polynomials
(http://www.zib.de/koepf/isaac.html)
at the First ISAAC Congress
(http://www.math.udel.edu/isaac/conferen/congr97.htm),
with the emphasis on the use of computer algebra. This congress took place
at the University of Delaware, Newark, Delaware, June 3-7, 1997. In this
special issue of the Journal of Symbolic Computation we would like to
collect articles about the interaction between computer algebra and
orthogonal polynomials and special functions. Hopefully, the participants
of Session 13 at the First ISAAC Congress will submit papers, but this
special issue is open for everybody. Rather than a Proceedings of a
session, the issue is meant as a state of the art account of this topic.
Contributions should discuss non-trivial usage of symbolic computation
which significantly contributes to the theory of Orthogonal Polynomials
and Special Functions. Examples of categories in which contributions may
fall are:
- New symbolic algorithms for obtaining specific results in OP & SF. This
may also be a presentation of a drastically improved implementation of an
existing algorithm.
- Proofs aided by symbolic computation of significant new results in OP &
SF which are yet intractable by purely human effort.
- New significant results in OP & SF which are finally provable without
computer aid, but which would have been hard to find without
experimentation by symbolic computation. The description of this
experimentation should be illustrative for future efforts by others.
- Aspects of symbolic computation in connection with the production of
on-line text books and formula dictionaries on OP & SF.
Authors are invited to submit their manuscripts to the Managing Guest
Editor, Wolfram Koepf, who will handle the preparation of this special
issue, preferably by e-mail in some TeX dialect, or in PostScript. All
submitted papers will be refereed according to the JSC usual refereeing
process (see http://www.cis.udel.edu/~caviness/jsc.html for information
about JSC). The journal's LaTeX style file can be obtained from
ftp://ftp.udel.edu/pub/jsc (America) or
ftp://ftp.risc.uni-linz.ac.at/pub/jsc (Europe).
Important dates:
Deadline for submission of full papers: 15 January, 1998
Notification of acceptance/rejection: 31 May, 1998
Final revised manuscripts due: 15 September, 1998
Appearance of special issue: 1998/1999
Guest editor addresses:
Wolfram Koepf Richard A. Askey
http://www.zib.de/koepf/ http://conley.math.wisc.edu/~askey/
Konrad-Zuse-Zentrum Berlin University of Wisconsin
Takustr. 7 Department of Mathematics
D-14195 Berlin-Dahlem 480 Lincoln Drive
Germany Madison, WI 53706-1313, USA
koepf@zib.de askey@math.wisc.edu
Tom H. Koornwinder
http://turing.wins.uva.nl/~thk/
Department of Mathematics
University of Amsterdam
Plantage Muidergracht 24
NL-1018 TV Amsterdam
The Netherlands
thk@wins.uva.nl
Topic #12 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Wolfram Koepf
Subject: Maple and REDUCE Packages on q-Hypergeometric Summation
Editors' Note: This announcement is reprinted from our Newsletter, June
1997.
Careful implementations of the q-versions of Gosper's and Zeilberger's
algorithms for indefinite and definite summation [2] are available in
REDUCE [1] and Maple from Wolfram Koepf (koepf@zib.de). These
implementations allow input in the usual notation, using q-Pochhammer
symbols, q-binomial coefficients, q-hypergeometric terms, etc., and they
support a posteriori proofs of the resulting terms and recurrence
equations, respectively.
These packages have been implemented by Harald Boeing under the
supervision of Wolfram Koepf and can be obtained by request
(boeing@zib.de, koepf@zib.de).
The REDUCE package QSUM will be part of the next REDUCE Version 3.7, and
the Maple package qsum.mpl (working with version V.3 and V.4) will be
submitted to Maple's share library.
[1] Boeing, H., Koepf W.: REDUCE package for the indefinite and definite
summation of q-hypergeometric terms. Konrad-Zuse-Zentrum Berlin (ZIB),
Technical Report TR 97-04, 1997.
[2] Koornwinder, T. H.: On Zeilberger's algorithm and its q-analogue: a
rigorous description. J. of Comput. and Appl. Math. 48 (1993), 91-111.
Topic #13 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Semen Yakubovich
Subject: Project at Leuven on integral transformations
Since January 6, 1997 Dr. S.B. Yakubovich is staying in Leuven (Belgium)
for one year on a sabbatical leave from the Belarusian State University of
Minsk, Belarus. He was invited by the Katholieke Universiteit Leuven and
its Department of Mathematics to work with Professor Walter Van Assche in
the framework of the Askey-Bateman project of special functions and
integral transformations.
Addresses for contacts:
Department of Mathematics
Katholieke Universiteit Leuven
Celestijnenlaan 200 B
B-3001 Heverlee (Leuven)
Belgium
e-mail: semen@wis.kuleuven.ac.be
Topic #14 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Tom Koornwinder
Subject: Positions at Kyushu University
K. Mimachi informed me about research
instructor positions at the Graduate School of Mathematics of the Kyushu
University (Fukuoka, Japan).
Since these positions are open for mathematicians of all kinds of
specialization, not necessarily in Orthogonal polynomials and Special
functions, I will not give any details here, but just refer interested
people to the full advertisement at
http://turing.wins.uva.nl/~thk/links/fukuoka
Topic #15 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Wolfram Koepf
Subject: Russian Newsletter on Integral Transforms and Special Functions
Editors' Note: This announcement is reprinted from our Newsletter, June
1997.
At the end of 1996 the first issue of a new Russian Newsletter on Integral
Transforms and Special Functions appeared. This Newsletter is generally in
Russian language with some English material though. I am pleased that the
Russian group around A. P. Prudnikov found our lay-out promising, and
adapted it accordingly. You will find the first page of their newsletter
reprinted on the back cover of the June 1997 issue of our Newsletter. I
will try to reprint articles that might be of interest to the members of
our group in English language.
Topic #16 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: A. P. Prudnikov
Subject: New Book Series
Editors' Note: This announcement is reprinted from our Newsletter, June
1997.
New Book Series:
Analytical Methods and Special Functions
Editors: A. P. Prudnikov, C. F. Dunkl, H.-J. Glaeske, M. Saigo
Gordon and Breach Science Publ. for Mathematics, Singapore
The aim of this series is the presentation of research activities in
analytical methods of analysis, including integral transforms, special
functions, series expansions, approximation theory, asymptotic analysis,
operational calculus, integral equations, ordinary and partial
differential equations, perturbation methods and other special analytical
methods in problems of pure and applied mathematics, biological and
physical sciences and engineering.
The series will be a companion series to the existing journal Integral
Transforms and Special Functions.
The first book of this series appeared in 1996:
Volume 1: Series of Faber Polynomials.
By P. K. Suetin, Technical University of Communication and Informatics,
Moscow, Russia
December 1996, 320 pp., ISBN 90-5699-058-6
The book contains some of the most important classical and modern results
on the series of Faber polynomials and their applications.
Interest in this subject area has rapidly increased over the last decade,
yet the presentation of research has been confined mainly to journal
articles. Analysis of recent results concerning the theory and application
of Faber series shows that these are, at present, a very important object
of study in the theory of functions of complex variables, and a convenient
investigative tool in the theory of analytic function approximation, as
well as in some questions of numerical analysis.
Contents:
Some results of approximation theory
The elementary properties of Faber polynomials
Faber series with the simplest conditions
Asymptotic properties of Faber polynomials
Convergence of Faber series inside a domain
Series of Faber polynomials
Some properties of Faber operators
Faber series in a closed domain
Faber polynomials and the theory of univalent functions
Faber series in Canonical domains
Faber series and the Riemann boundary problem
The summation formula of Dzyadyk
Generalization of Faber polynomials and series
Some recent results.
Forthcoming volumes:
B.G. Korenev. Bessel Functions and Their Applications.
S.G. Samko. Hypersingular Integrals and Their Applications.
A.M. Sedletskii. Fourier Transforms and Approximations.
P.K. Suetin. Orthogonal Polynomials in Two Variables.
V.A. Yurko. Inverse Problems for Differential Operators.
Topic #17 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Nico Temme
Subject: Book on Umbral Calculus
Editors' Note: This book announcement is reprinted from our Newsletter,
June 1997.
Probabilistic and Analytical Aspects of the Umbral Calculus
By A. Di Bucchianico
CWI Tract 119, ISBN 90 6196 471 7, 1997, 148 pp.,
CWI, Amsterdam, The Netherlands, Price: NLG 35.00
The subject of this tract is a class of sequences of polynomials
{q} defined by the following functional equations
q_{n}(x+y) = sum(k=0 to n) q_{k}(x) q_{n-k}(y) (n=0,1,...) (1)
A sequence of polynomials that satisfies (1) is called a sequence of
polynomials of convolution type. These sequences are closely related to
the sequences of polynomials of binomial type introduced by Rota, i.e.,
sequences of polynomials {p} satisfying
q_{n}(x+y) = sum(k=0 to n) {n choose k}q_{k}(x)q_{n-k}(y) (n=0,1,...) (2)
The sequence {x^n, n in N} is of binomial type by the Binomial Theorem,
which explains the name binomial type. In this tract sequences of
polynomials of convolution type are studied instead of sequences of
polynomials of binomial type because convolution is a fundamental
operation in analysis and probability theory. The binomial convolution
appearing in (2) has advantages when dealing with certain combinatorial
problems.
An extension of the class of sequences of polynomials of
binomial/convolution type is the class of Sheffer sequences {s}, whose
convolution type version is defined by
s_{n}(x+y) = sum(k=0 to n) s_{k}(x) q_{n-k}(y) (n=0,1,...) (3)
for some fixed sequence {q} of convolution type. The class of Sheffer
sequences includes (amongst others) the Hermite, Bernoulli and Laguerre
polynomials.
The history of Sheffer sequences goes back to 1880 when Appell studied
sequences {a} of polynomials satisfying D a_{n} = n a_{n-1} (D is the
differentiation operator). Appell showed that these sequences satisfy
a_{n}(x+y) = sum(k=0 to n) {n choose k} a_{k}(x) y^{n-k} (n=0,1,...) (4)
These sequences are called Appell sequences nowadays. The Hermite
polynomials form an Appell sequence.
A survey of the Umbral Calculus with over 400 references can be obtained
in electronic form through the Electronic Journal of Combinatorics:
http://ejc.math.gatech.edu:8080/Journal/Surveys/index.html
Contents:
Chapter 1. Introduction.
Chapter 2. Umbral Calculus.
Chapter 3. Applications of the Umbral Calculus.
Chapter 4. Banach Algebras.
Chapter 5. Central limit theorems and infinite divisibility.
Bibliography (253 items).
Index.
Topic #18 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Wolfram Koepf
Subject: New Journal: Inequalities and Applications
Inequalities and Applications
Editor-in-chief: Ravi P. Agarwal
The Gordon and Breach Publishing Group, Singapore, 4 issues per volume,
approximately 100 pages per issue, ISSN 1025-5834
The aim of this journal is to provide a multi-disciplinary forum of
discussion in mathematics and its applications in which the essentiality
of inequalities is highlighted. Areas covered include inequalities in
analysis, approximation theory, calculus of variations, combinatorics,
economics, geometry, mechanics, optimization, and probability theory.
This journal accepts high quality papers containing original research
results and survey articles of exceptional merit. Subject matters should
be strongly related to inequalities, such as, but not restricted to, the
following list.
Inequalities in Analysis
Inequalities in Approximation Theory
Inequalities in Calculus of Variations
Inequalities in Combinatorics
Inequalities in Economics
Inequalities in Geometry
Inequalities in Mechanics
Inequalities in Optimization
Inequalities in Probability Theory
Editorial Board:
J. Aczel, C. Bandle, P. Bullen, W. Desmond Evans, W.N. Everitt,
A.M. Fink, R. Ger, R.P. Gilbert, R. Glowinski, V.B. Kolmanowskii,
M.A. Krasnosel'skii, A. Kufner, V. Lakshmikantham, P.L. Lions,
L. Losonczi, E.R. Love, K. Masuda, J. Mawhin, R. Mennicken,
G.V. Milovanovic, R.N. Mohapatra, R.J. Nessel, T.M. Rassias,
S. Saitoh, G. Talenti, K.L. Teo, W. Walter, A. Zettl.
If you are interested in submitting a paper for publication please contact
Ravi P. Agarwal
Department of Mathematics
National University of Singapore
101 Kent Ridge Crescent
Singapore 119260
The World Wide Web home page of the journal is
http://www.gbhap.com/journals/290/290-top.htm
Topic #19 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Hans Haubold
Subject: Books on Special Functions in Astrophysics and Cosmology
Editors' Note: This announcement is reprinted from our Newsletter, June
1997.
I would like to announce that I have still some free copies of the
following books:
Gottloeber, S., Haubold, H. J., Muecket, J.-P. and Mueller, V.: Early
Evolution of the Universe and Formation of Structure. Akademie-Verlag,
Berlin, 1990.
Mathai, A. M. and Haubold, H. J.: Modern Problems in Nuclear and Neutrino
Astrophysics. Akademie-Verlag, Berlin, 1988.
in which special functions are applied to problems in astrophysics and
cosmology.
Members of the Activity Group who would like to receive one of these books
(or both) should send me an e-mail message
(haubold@ekpvs2.dnet.tuwien.ac.at), and I will air mail them the desired
books.
Furthermore I would like to ask whether somebody knows recent articles in
which Meijer's G-functions or Fox's H-functions are used in connection
with problems in astrophysics or cosmology. Any information in this
direction would be appreciated.
Topic #20 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Jet Wimp
Subject: Review of Gradshteyn and Ryzhik
Editors' Note: This review is reprinted, with permission, from the
American Mathematical Monthly, April 1997. We have already published a
short review by Marvin Rosenbaum of the CD-ROM version in OP-SF NET 3.6,
Topic #12. Information on ordering the CD-ROM version was given in
OP-SF NET 3.1, Topic #14 (revised in OP-SF NET 3.2, Topic #5).
Review of Tables of Integrals, Series and Products
by I. S. Gradshteyn and I. M. Ryzhik, edited by Alan Jeffrey
Updated, 5th Edition, CD Rom Version 1.0
Academic Press, New York (1996)
reviewed by Jet Wimp
I _adore_ GRJ (Gradshteyn, Ryzhik and Jeffrey), all 1200 pages of it. I
have two copies: one for the office, one for home. If my upper body
musculature were better developed, I would carry it to Europe with me, to
Asia, to the Himalayas. Though some worthwhile identities are missing,
for instance, those relating to differential and difference properties of
hypergeometric functions, GRJ can serve as a near equivalent to the
combined five volumes in the Erdelyi set [1,2]. It's the ideal desert
island book, though of course one has to get it there, and it may not be
easy explaining to one's ex-shipmates why this hefty and venerable tome
should be given precedence over that mouldy goatskin flask of water when
planning the contents of the lifeboat.
Let me talk a bit about this volume, the book, not the current CD.
Though called, modestly, "Table of Integrals, Series, and Products," that
doesn't begin to do justice to its contents. The appellation "sums"
covers closed-form expressions of frequently occurring sums along with
convergence material on infinite sums. These topics, and products,
functional series, asymptotic series, formulas from differential calculus,
comprise the introductory chapter, the 0th chapter of the volume. Also
materializing in this chapter are some of those hoary, cabalistic
functions that used to inhabit our mathematical books, but no longer do:
the Gudermannian, Lobachevsky's "angle of parallellism."
The first chapter is a treatment of elementary functions so
comprehensive it will allow the owner to ditch those tattered trig tables.
The second, third and fourth chapter deal with definite and indefinite
integrals of elementary functions, and the fifth, sixth, and seventh deal
with definite and indefinite integrals of special functions. Of course, to
make the book self-contained, a discussion of special functions is
required, and this the book has, in spades. Its eighth and ninth chapters
comprise a wonderful 200 page treatment of all the standard higher
functions, and many of the results given there are absent from the Erdelyi
volumes -- indeed, absent from any mathematical treatment commonly
available. The formulas are a lot of fun to read, and one can,
Jeopardy-like, shield from view the left hand side of an equation and ask
what the right hand side represents, for instance:
ANSWER:
The series sum_{k=0 to infty) c_k z^k, |z| < 2 where
c_{n+1} = [1/(n+1)]sum (k=0 to infty) (-1)^{k+1}s_{k+1}c_{n-k}, n =
0,1,2..., with c_0 =1, s_1 = gamma = .57721..., s_n = zeta(n), n = 2,3,...
QUESTION: What is Gamma(z+1)?
There are several supplementary chapters that practicing
mathematicians will consider pure gold: a chapter on vector field theory,
one on algebraic inequalities, one on integral inequalities, a chapter on
matrices, one on determinants, one on norms, one on ordinary differential
equations, and, to cap it off, a chapter containing Mellin, Fourier, and
Laplace transforms; this chapter is vestigial, though, and doesn't offer a
viable alternative to the standard tables [4,5,6].
The earlier editions had gobs of mistakes, but thanks to dedicated
readers who filed their emendations with the editor, with the fifth
edition most of the mistakes have been weeded out. I found one though (I
almost had to justify my credentials for writing this review.) The power
beta on the right hand side of the transformation formula for the Appell
function F_4, formula 3 on page 1083, should be -beta.
Where, in its comprehensiveness, does this volume stand, in
comparison to other books? Well, it far surpasses the quaint hand-written
2 volume 1965 table of integrals of Groebner and Hofreiter [3]. The
transform sections, as pointed out, suffer in comparison to other tables.
It certainly contains far less material than the mammoth five-volume set
by Prudnikov and others with its 3500 pages of material [7]. The scope of
[7], though, probably exceeds what anyone will ever require. The reader
may know of the Borges short story, "The Library of Babel" in which the
author envisions a library whose first room contains a hundred or so
books, the first containing a single page with the single letter "A", the
second a page with the single letter "B," etc. The second room of the
library starts with a book containing a single page with the letters "AA,"
followed by a book containing "AB,... ." I'm sure the reader gets the
idea. Any desired text you want will be somewhere in that library; the
problem is only one of information retrieval. The Prudnikov volumes come
close to being a mathematical equivalent to Borges' imaginary construct.
And the _presentation_ of the GBJ book: the binding, the
appearance, the typography are all splendid. Remember the shabby photo
offset reproductions of Russian books that held us hostage twenty or so
years ago -- the malodorous books on oatmeal colored paper with the
English intertext and the Cyrillic formulas? Nothing could be
aesthetically more distant from those books than this. Academic Press has
compiled a gorgeous volume. Naturally, I can think of things that should
have been included that weren't, but when I am searching for a formula
vital to some research objective, it's surprising how often it can be
found in GRJ.
So what more remains to be said? Well, there's the old joke about
the play heavily revised in tryouts in Philadelphia and Boston, and the
producer saying to the playwright after a disastrous Broadway opening
night, "You just died from improvement." Could this CD sound the death
knell of a wonderful publishing concept?
On the drawing board, it must have seemed like a marvellous idea.
A hugely popular enchiridion: let's make it available to anyone at the
flick of a computer key. Lets make a CD out of it! Academic enlisted the
talents of Lightbinders of San Francisco, who produced the CD using the
opulent and flexible text display software called DynaText 2.3. I was
impressed with the software, which might be a wonderful way to render some
books computer accessible. But here, no. What went wrong? The very worst
thing that could go wrong. _You_can't_see_the_formulas!_ They are tiny,
tiny, tiny. (Ed's note: In the original review the words "tiny, tiny,
tiny" were in progressively smaller fonts.) The liner notes for the CD
cautioned that the reader should have Adobe File Manager to properly view
the formulas. I ordered it. It helped not at all. One can do a mouse click
in the upper right hand corner and things enlarge a bit, but not enough.
I noticed how Academic, perhaps responding to an increasingly
litigious society, had included in the flyleaf of the original book a
warning:
"Academic Press and the editor have expended great effort to
ensure that the material presented in this volume is correct.....
However.... neither Academic Press nor the editor shall be
responsible for any errors, omissions, or damages arising from the
use of this volume."
If this warning was ever warranted, it was in the liner notes of this CD.
Damages, indeed. I estimate the chances of retrieving a correct formula
from the screen display at about one out of three, that is, for anyone
lacking microfocal vision. Now I was doing all this on a Mac platform;
maybe someones DOS or Windows equation was lushly readable, elegant,
utile. If so, I offer my humblest apologies to Academic; my hearty
congratulations go to any such customers. They may imagine themselves
fortunate but, computer karma being what it is, they'll soon enough be
victims to some other piece of flawed software.
I phoned customer support at Lightbinders, and there followed one
of those Kafkaesque conversations that seem to be so much a feature of the
computer age. "You can display the TeX representation of an equation," the
consultant pointed out. "Then you can paste the equation into a TeX
document." But copying by highlighting the selection didn't work. "Hmmmm,"
the consultant said. "Do a copy from the file menu," he ordered. It didn't
work. "HHMMMM," he said. "Do a copy by depressing the command and C keys."
No luck. ``HHHMMMMMMMMM," he said. "_That's_strange_". There I was,
facing this travesty of the desired equation, staring at me in its TeX
metamorphosed form. Has the reader ever tried to reconstruct an equation
from its TeX representation? Don't. It's easier to _derive_ the equation.
One of my favorite equations, a darling little double integral for an
Appell function, had become a sixteen-line porridge of "{}}}{}}{"s and
"//\/\/\/"s . One can print the whole page containing the equation in
question, but before one would do this, one would want to know what the
equation says. The pericopes on notations and index of special functions
look like so much flypaper. From the customer rep I got no satisfaction,
and I was reminded of those primitive tribes where half the members speak
one language, the other half another.
What else could go wrong? Something else did. You cant _find_
things. The list of contents is too abbreviated, consisting only of the
chapter headings in the book; further details require clicking the mouse
on the displayed headings. Once again, a Catch-22. You have to know where
something is to find it. Where should you look for the definition of
Euler's constant? In the introduction? In the definition of elementary
functions? In the integral tables? No, far away in Chapter 9, Special
Functions, buried several layers deep. The table of contents of the book,
the honest to god paper book, has to be visually scanned too, but it is
all in front of you: nothing is buried under something else. After
struggling with the CD-ROM, I clutched my book to my chest, praying it
would never go away.
Also, the software may have corrupted my system file, entailing a
trek to the computer services center four city blocks away and, after I
discovered the computer hardware was intact, a trek back to install the
system software, However, I make no accusations. Those ethereal and subtle
software incompatibilities may be the only true things of the spirit, the
only mysteries, vouchsafed to to a technocratic society barreling into the
21st century. Let us revere them.
I love books, but I'm not a Luddite. I embrace software that
works. Macbeth spoke of someone being yanked untimely from his mother's
womb, and I think that software -- market pressure, no doubt -- is often
yanked untimely from the designer's noggin. If you're planning on adding
this CD to your library, beware. Be certain your computing platform
accommodates it in a way that makes it legible, convenient and system
compatible. Take nothing for granted. A hasty purchase means a wracking
day on the phone to some callow customer rep in some distant part of the
country, and no concomitant satisfaction.
REFERENCES
[1] Erdelyi, A, et al, Higher transcendental functions, 3 v., McGraw-Hill,
New York (1953).
[2] Erdelyi, A, et al, Tables of integral transforms, 2 v., McGraw-Hill,
New York (1954).
[3] Groebner, W., and N. Hofreiter, Integraltafel: erster Teil,
Unbestimmte Integrale; zweiter Teil, Bestimmte Integrale, Springer-Verlag,
Wien (1965)
[4] Oberhettinger, F., Tabellen zur Fourier Transformation,
Springer-Verlag, Berlin (1957).
[5] Oberhettinger, F., Tables of Bessel transforms, Springer-Verlag, New
York (1972).
[6] Oberhettinger, F., and L. Badii, Tables of Laplace transforms,
Springer-Verlag, New York (1973).
[7] Prudnikov, A. P., Yu. A. Brychkov, and O. I. Marichev, Integrals and
series, 5 v., Gordon and Breach, New York (1986).
Topic #21 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Vadim I. Zelenkov and
Vadim A. Savva
Subject: VI International Krawtchouk Conference: Kiev, Ukraine, May 14-17,
1977
Editors' Note: This report is reprinted from our Newsletter, June 1997.
The number of classical orthogonal polynomials systems of a discrete
variable is highly restricted, hence each discoverer of such an OPS
deserves to be known to the scientific community not only as a
mathematician but also as an individual. That's why it is very strange to
find only some morsels of information about the author of "Sur une
generalisation des polynomes d'Hermite" published in 1929 which initiated
a new stage in the theory of orthogonal polynomials.
The reason is both simple and tragic.
Mykhailo Pilipovich (in Ukrainian; in Russian his name is sounded Mikhail
Philippovich) Krawtchouk was born on September 27, 1892 in the small
village of Chovnitsy (Western Ukraine). After graduating from gymnasium he
entered Kiev St. Vladimir University, obtaining his first diploma degree
in 1914---on the eve of the First World War. Thus the young mathematician
had to move to Moscow because of the University evacuation. On September
5, 1917 (80 years ago) he gave his first lecture.
After the 1917 revolution, M. Krawtchouk worked in various Kiev
universities, institutes, gymnasia, then for two years of the civil war
(1919-1921) he was the head of a rural school near Kiev.
When the situation in the then USSR became relatively stabilized,
Krawtchouk got the opportunity for fruitful scientific work. The title of
his doctoral thesis was "On Quadratic Forms and Linear Transform" (1924).
He took part in the International Mathematical Congresses in Toronto
(1924) and Bologna (1928), had close contacts with Hadamard, Hilbert,
Courant, Tricomi, i.a. In 1929 he became a full member of the
All-Ukrainian Academy of Sciences.
The list of M. Krawtchouk's scientific works contains about 180 titles
including such branches of mathematics as the theory of permutation
matrices, theory of algebraic, transcendental, differential and integral
equations, introduction and use of polynomials associated with the
binomial distribution (Krawtchouk polynomials), etc. Moreover his efforts
were applied in the fields of philosophy, history of mathematics and
mathematical education. It is especially important for the independent
Ukraine that it was M. Krawtchouk who was in charge of editing the first
three-volume dictionary of Ukrainian mathematical terminology. (Having a
knowledge of French, German, Italian, Polish and, of course, Russian, he
delivered lectures and wrote articles mostly in Ukrainian).
Anyone knowing even a little Soviet history of the thirties can conclude
that Krawtchouk could not avoid the Great Terror. During the Orwellian
"hours of hatred" in 1937 he was being denounced as a "Polish spy",
"bourgeois nationalist" etc. In 1938, he was arrested and sentenced to 20
years of confinement and 5 years of exile.
Academician Krawtchouk, the author of the results which became part of the
world's mathematical knowledge, the brilliant lecturer who inspired many
outstanding followers (e.g., Sergey Korolev, the future leader of the
Soviet space programme), the member of the French, German and other
Mathematical Societies died on March 9, 1942 in Kolyma branch of GULAG
(North-Eastern Siberia) more than 6 months short of his 50th birthday.
M. Krawtchouk was officially rehabilitated in 1956 and restored as a
member of the Academy of Sciences only in March 1992, 50 years after his
death.
Tempora mutantur, the times are changing, and in September 1992 the First
International M. Krawtchouk Conference was held in the Ukraine. Since then
such conferences have been held yearly.
The 6th International Scientific Krawtchouk Conference took place in Kiev
from May 15th to 17th, 1997. The organizers were the Ukrainian Ministry of
Education, Institute of Mathematics, National Academy of Sciences of
Ukraine and National Technical University of Ukraine (formerly Kiev
Polytechnical Institute where M. Krawtchouk in his time was the head of
the Mathematical Chair).
The opening ceremony included speeches from members of the Organizing
Committee, addresses from M. Krawtchouk's relatives and followers and some
splendid Ukrainian songs executed by a chorus.
The scientific agenda consisted of about 380 reports divided into four
sections according to Krawtchouk's scientific interests: Differential and
Integral Equations, their Application; Algebra, Geometry, Mathematical and
Numerical Analysis; Probability Theory and Mathematical Statistics;
History and Teaching Methods of Mathematics. Most of the participants
represented the Ukraine, 19 reports were from Russia, 4 from Belarus and 1
from the Czech Republic. Many participants were postgraduates and young
scientists presenting their first results.
Let us mention some of the titles which could be of interest to the
readers of the Newsletter:
V. Gaidei: Generalised m-Lommel-Bessel-Maitland Functions. Properties
and Application.
V. Zakharov: New Special Function _4F_1^4 of Four Arguments.
V. Savva, V. Zelenkov: Orthogonal Krawtchouk Polynomials and Exact
Solutions for the Dynamics of Multilevel Systems in Radiation
Field.
V. Zelenkov, V. Savva: Peculiarities of the Dynamics of Krawtchouk
Quantum Systems with Degenerate Levels.
O. Kuzhel: Recursion Relations for the Euler-Bernoulli Numbers.
D. Leykin: Addition Theorems for the Hyperelliptic Kleinian
Functions.
Ya. Mamteev, V. Stukalina, T. Huchraeva: Modified Struve Function.
L. Ostrovetskyi: On Some Analytic Functions Approximation with
Algebraic Polynomials.
O. Papanova: On the Zeroes of P_nu^mu (x)
Most of the conference materials have been published in Ukrainian; some of
them are in Russian and some in English.
An additional circumstance which made the conference especially attractive
was the pleasant weather and the famous Kiev chestnut trees blooming on
schedule in May. We were impressed by ancient Kiev though we had visited
it repeatedly before (Belarus is not so far from the Ukraine!).
The participants are grateful to the Organizing Committee led by
Academician M. Zgurovskyi and especially to Professor Nina Virchenko who
carried out enormous work. Moreover, for about thirty years she has
studied the biography of M. Krawtchouk and the authors of this report
would like to express their personal thanks for the permission to use some
of her articles while preparing this text.
The details of the 7th Krawtchouk Conference (1998) are now under
discussion. You can send your inquiries to the address:
Professor Nina Virchenko
Dept. of Mathematics No. 1
National Technical University of Ukraine (KPI)
37, Peremogi Avenue
252056, Kiev, Ukraine.
Topic #22 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: Charles Dunkl
Subject: Report on Madison Centennial Conference
Editors' Note: This report is reprinted from the June Newsletter
Report on Ph. D. Centennial Conference, Department of Mathematics,
University of Wisconsin-Madison, May 22-24, 1997
This conference was organized to celebrate the hundredth anniversary of
the first granting of the Ph.D. in Mathematics by the university.
Announcements were sent to the former students and friends of the
department and produced a good turn-out for the meeting. It was estimated
that 250 attended the opening reception, which was held in the wonderful
conference room on the ninth floor of Van Vleck Hall, overlooking the
lakes of Madison; and 375 attended the banquet. Current (or recently
retired) faculty members who are well-known for their work in special
functions, or the use of special functions in harmonic analysis, include
Dick Askey, Walter Rudin and Steve Wainger. The format of the meeting
consisted of 45-60 minute talks in the mornings mostly with historical
emphasis and many parallel minisymposia in the afternoons. Walter Rudin
gave the first lecture, titled "Harmonic Analysis at Wisconsin"; he
discussed the original motivating examples of vibrating string problems,
expansion problems which led to theories of integration, and then the
modern era of Calderon-Zygmund singular integrals, Eberlein's almost
periodic functions, Askey and Wainger's transplantation theorems, and
analytic functions of several variables.
Alan Schwartz and the undersigned are two of Rudin's students who are
working in harmonic analysis and special functions. Dick Askey lectured on
"Special Functions in Wisconsin" the second morning. He defined special
functions as those which occur often enough to need a name (he has
previously called them "useful functions"). The first Ph.D. thesis in this
area may have been the one by F.T. H'Doubler in 1910, concerning
functional equations and theta functions. More recently Jaap Korevaar (now
in Amsterdam) wrote a paper on Fourier transforms and Hermite polynomials
and directed Gil Walter's thesis in 1962. Loyal Durand of the Wisconsin
physics department also studied Bessel functions. H.S. Wall was a Ph.D.
student of E. Van Vleck and studied q-Laguerre polynomials (1927). Other
significant results in the field which have Wisconsin connections include
Schoenberg's paper on positive-definite functions on spheres, the
Askey-Gasper inequality instrumental in de Branges' proof of the
Bieberbach conjecture, and Berndt's commentaries on Ramanujan's notebooks.
Askey discussed work by some of his students - Jim Fitch, Dennis Stanton,
Jim Wilson, Warren Johnson and Walter "Chip" Morris.
There were ten lectures in the special function minisymposium (organized
by Dunkl and Askey), four on Friday and the remainder on Saturday; here is
a list of speakers and brief descriptions of the talks:
- Gilbert Walter: a comparison between series expansions and other
properties of special functions and wavelets;
- Steve Milne: a new result on counting solutions of the Diophantine
equation x_1^2+x_2^2+...+x_s^2=m for given m when s=4n^2 or
s=4n(n+1) for some integer n;
- Alan Schwartz: classification of polynomial hypergroups in one or two
variables, with examples coming from Jacobi and disk polynomials;
- Charles Dunkl: an overview of orthogonal polynomials in $N$ variables
for weight functions which are invariant under the symmetric or
hyperoctahedral groups;
- George Gasper: summation formulas for a type of q-Kampe de Feriet
function, related to a q-version of {9-j} symbols;
- Paul Terwilliger: a new and improved approach to the structure theorem
for Leonard systems and Askey-Wilson polynomials, in the context of
type P and Q association schemes;
- Anatol Kirillov: quantum algebra versions of Schur functions and
Schubert polynomials (q-alg/9701005);
- Mourad Ismail: asymptotics for zeros and recurrence coefficients for the
family of orthogonal polynomials for weights of the form exp(-u(x)),
x in R where u'(x) is convex and u(x) -> infty as x -> +-infty;
this includes u(x)=x^{2n};
- Dennis Stanton: a self-contained and conceptual proof of some identities
of the form _5F_4(*)=0 which were originally stated and proven by
George Andrews;
- Sergei Suslov: a basic analog of Fourier series; joint work with Joaquin
Bustoz.
The attendance at the minisymposium varied from 15 to 25, a consequence of
the fact that there were as many as 16 parallel sessions. This report, of
course, has singled out the special functions influence of the faculty and
students (in a broad sense: past and present, postdocs, visitors as well
as senior professors) of the University of Wisconsin. The organizers
estimate that 900 doctorates have been granted by the department in the
period 1897-1997 with about 370 in the peak years 1962-1977. Many workers
in special functions have some connection with Wisconsin and it would be a
major project to describe completely the impact that has been made on the
field by these people.
Charles F. Dunkl
Topic #23 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: OP-SF Net editors
Subject: ftp site for papers in Orthogonal Polynomials and Special
Functions
Hans Haubold's ftp archive for preprints in the area of Orthogonal
Polynomials and Special functions is the continuation of Waleed Al-Salam's
preprint archive. One can approach the archive by anonymous ftp to
unvie6.un.or.at, directory siam. Very recently, Hans Haubold has
constructed a convenient WWW interface for this ftp site, at the address
ftp://unvie6.un.or.at/siam/opsf_new/00index.html
See OP-SF Net 4.3, Topic #12 for more features of this interface.
Between 6 May and 9 July 1997, the following paper in the archive was
updated:
G. Gasper and M. Rahman, Errata, updates of the references, etc. (as of
May 16, 1997) for the book: Basic Hypergeometric Series, by George Gasper
and Mizan Rahman, Encyclopedia of Mathematics and its Applications, Vol.
35, Cambridge University Press, Cambridge - New York, 1990. xx+287 pp.
ISBN 0-521-35049-2. (see siam/opsf_new/gasper/gasper2.tex and
siam/abstracts_new/gasper.abstract.html)
Two further abstracts were deposited in the submissions directory:
R. Gorenflo and F. Mainardi :
"Fractional Oscillations and Mittag-Leffler Functions", pp. 22 (1996)
Preprint No. A-14/96, Freie Universitaet Berlin, Serie A Mathematik
abstract: ftp://unvie6.un.or.at/siam/submissions/gorenflo_mainardi.abs)
full paper: http://www.math.fu-berlin.de/publ.index.html
H.T. Koelink,
"Basic Lommel polynomials",
July 1997, report 97-07 Universiteit van Amsterdam, pp. 16
abstract: ftp://unvie6.un.or.at/siam/submissions/koelink.abs
full paper:
ftp://www.wins.uva.nl/pub/mathematics/reports/Analysis/koelink/basiclommel.ps
Topic #24 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: The Editors ,
Subject: Changes of Address, WWW Pages, etc.
Neil J.A. Sloane (AT&T Labs-Research) has his home page at
the URL: http://www.research.att.com/~njas/index.html
In particular see Sloane's On-Line Encyclopedia of Integer Sequences at
the URL: http://www.research.att.com/~njas/sequences/index.html
and his actual Data Base of Integer Sequences at
the URL: http://www.research.att.com/~njas/sequences/eisbt0fry.html
Joris Van der Jeugt (Universiteit Gent, Belgium) has his home page at
the URL: http://allserv.rug.ac.be/~jvdjeugt/
Hjalmar Rosengren (Lund University, Sweden) has his home page at
the URL: http://www.maths.lth.se/matematiklu/personal/hjalmar/engHR.html
Topic #25 -------------- OP-SF NET 4.4 ------------- July 15, 1997
~~~~~~~~~~~~~
From: OP-SF Net editors ,
Subject: Obtaining back issues of OP-SF Net and submitting contributions
to OP-SF Net and Newsletter
Back issues of OP-SF Net can be obtained from
ftp: ftp.wins.uva.nl, in directory
pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir
or WWW: http://turing.wins.uva.nl/~thk/opsfnet/
or WWW: http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html
Contributions to the OP-SF Net 4.5 should reach the email address
poly@siam.org before September 1, 1997.
The Activity Group also sponsors a (printed) Newsletter edited by Wolfram
Koepf. Deadline for submissions to be included in the October 1997 issue
is September 15, 1997.
Please send your Newsletter contributions directly to the Editor:
Wolfram Koepf
Konrad-Zuse-Zentrum
Takustr. 7
D-14195 Berlin-Dahlem, Germany
tel.: +49-30-841 85-348/347
fax: +49-30-841 85-269/125
email: koepf@zib.de
preferably by email, and in latex format. Other formats are also
acceptable and can be submitted by email, regular mail or fax.
Please note that submissions to the Newsletter (if not containing
mathematics symbols or pictures) are automatically considered for
publication in OP-SF Net, and vice versa, unless the writer requests
otherwise.
Previous issues of the Newsletter, but not the most recent one, can
be obtained as dvi or PostScript files from Wolfram Koepf's WWW homepage:
http://www.zib.de/koepf/
or by anonymous ftp at
ftp.zib.de in directory pub/UserHome/Koepf/SIAM
In order to join the SIAM Activity Group on Orthogonal Polynomials
and Special Functions, and thereby receive the Newsletter,
you have to become a member of SIAM. The annual dues are $93 for
SIAM plus $10 for the Group. Contact the email address join@siam.org .
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