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- November 9, 1995 -
- O P - S F N E T Volume 2, Number 6 -
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- Tom H. Koornwinder, Editor thk@fwi.uva.nl -
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- The Electronic News Net of the SIAM Activity Group -
- on Orthogonal Polynomials and Special Functions -
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- Please send contributions to: poly@siam.org -
- & address changes to: poly-request@siam.org -
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Today's Topics:
1. Introducing this issue and announcing our home page
2. Report on SIAM meeting, Charlotte
3. Al-Salam's ftp site transferred to Vienna
4. Procedure for new subscribers to OP-SF Net
5. Minisemester on Quantum groups and quantum spaces
6. 1-day conference Louvain-la-Neuve in honour of Professor Jean Meinguet
7. Session on Computational Harmonic Analysis and Approximation Theory
8. Joint summer reasearch conference on Random matrices etc.
9. XXI. International Colloquium on Group Theoretical Methods in Physics
10. Workshop Transform Methods & Special Functions, II (1996)
11. Death of Joe L. Ullman
12. Software Testing Service for Special Functions
13. Math Constants Web Resource
14. Gatteschi Festschrift
15. Special issue of Computers and Math. on Concrete Analysis
16. Impression from the Mittag-Leffler Institute, Sweden
17. New errata for the book Basic hypergeometric series
18. ftp and WWW addresses
19. Changes of address
20. New additions to Haubold's preprint archive
21. Obtaining back issues of OP-SF Net and submitting contributions
to OP-SF Net and Newsletter
Calendar of events: see issue/topic:
1995
November 27- December 1: main topic q-special functions in fourth week
of Warsaw Minisemester on Quantum groups and quantum spaces 2.6 #5
December 1: 1-day conference Louvain-la-Neuve in honour of Professor
Jean Meinguet 2.6 #6
December 18-22: International Conference on Harmonic Analysis, Delhi 2.5 #5
1996
January 10-11: Session on Computational Harmonic Analysis and
Approximation Theory, Orlando, Florida 2.6 #7
April 22-23: Umbral Calculus Special Session at MIT 2.4 #5
May 6-26: CRM Workshop on the Theory of Special Functions 2.1 #5
June 23-27: Joint summer reasearch conference on Random matrices,
statistical mechanics, and Painleve transcendents 2.6 #8
July 1-5: Meeting in Canterbury on Symmetries and Integrability of
Difference Equations 2.4 #6
July 15-20: International Colloquium on Group Theoretical Methods in
Physics, Goslar, Germany 2.6 #9
August 23-30: Workshop Transform Methods & Special Functions 2.6 #10
Topic #1 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: OP-SF Net editor
Subject: Introducing this issue and announcing our home page
There were quite a lot of new developments in the organisation of our
affairs during recent months. Waleed Al-Salam, who started the electronic
preprint archive on Orthogonal Polynomials and Special Functions in Alberta
and managed this archive for a couple of years, had to retire for reasons
of health. I want, on behalf of all of us, to express great thanks
for the service he has paid to our community in this way. I am also very
happy that Hans Haubold working at the United Nations in Vienna was
willing to continue this archive. Please find further information about
Haubold's archive in Topic #3.
Last month the publication of the Newsletter returned to a regular
schedule after a disruption caused by the resigantion of the previous
editor. As mentioned before, Wolfram Koepf from Berlin was willing to
take over as an editor. The first issue which appeared under his
editorship is really very worthwhile reading. If you want to give a
free copy of the next issue to a friend or want to put it in the
common room of your department, please contact Wolfram Koepf
.
Needless to say, your contributions to OP-SF Net and/or Newsletter
are always welcome. 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.
Our Activity Group has started its own home page at the World Wide Web.
The WWW address is:
http://www.math.yorku.ca/Who/Faculty/Muldoon/siamopsf/
At the moment Martin Muldoon is in charge of it.
If you may have already your own home page, you might consider to link it
to ours.
Then all members of the Activity Group will have received ballot forms
which they hopefully already returned. Whoever will have been chosen
by you, I am sure that the new group of officers will form an
active team which will serve your professional interests as much as
possible.
In the next topic Charles Dunkl reports on the recent SIAM annual
meeting in Charlotte: the minisymposium sponsored by us and the
business meeting of chairs of activity groups with the board of SIAM.
Your input is welcome on two matters mentioned there:
suggestions for contributions by our activity group at the Kansas City
SIAM annual meeting in July 1996, and feedback to Dan Lozier concerning
his proposal for a project to provide accuracy checks for special functions
algorithms on the Internet (see Topic #12).
Tom Koornwinder
Topic #2 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: Charles Dunkl
Subject: Report on SIAM meeting, Charlotte
Report on Annual SIAM meeting, Charlotte, North Carolina, October 23-26
Items pertinent to the activity group OP/SF at the business meeting
of chairs of Activity Groups with the board of SIAM:
- WWW page: SIAM is setting up links to home pages created by the
activity groups. Our group intends to start working on a home page
very soon (see Topic #1).
- 1996 annual meeting in Kansas City, Missouri, July - the theme has
been announced - it is "New Tools for Applied Mathematics". This
might be a good fit with the topic of the "Handbook" project (see
OP-SF Net 2.4, Topic #10) if one considers it as a method of using
modern media, such as CD-ROM, to disseminate information about special
functions. Furthermore, our group is encouraged to submit suggestions
for plenary speakers (45-minute lecture) for the meeting. Such
suggestions should be developed by December 15 (and can be sent to
Martin Muldoon ).
Observations at the minisymposium "Computational Aspects of Special
Functions and Orthogonal Polynomials" (see OP-SF Net 2.5, Topic #4
for the program):
-John Boyd (University of Michigan) talked about Hermite expansions,
the anharmonic oscillator, and perturbation theory.
- Walter Gautschi (Purdue U.) discussed an algorithm for generating
polynomials orthogonal with respect to a Sobolev norm. This theory has
significant differences from the ordinary one, for example, there is
no three-term recurrence.
- Dan Lozier (Nat'l Inst. of Standards and Technology) gave a survey
on software for special functions. He is working on a project to
provide accuracy checks for algorithms. The idea would be for
researchers to send in a list of pairs (x, f(x)) where f is a special
function, and then the NIST computers check these values independently
and generate an error report for the researcher. Dan has set up a Web
site and asks that the special function community read over his
suggestions and send feedback. See Topic #12.
- Nico Temme
(CWI, Amsterdam) talked about the problems of accurate computations of
probability distribution functions in regions of rapid increase, for
example, incomplete beta integrals with very large parameters. Often
such computations require much more work than routine problems.
- The writer of this note presented joint work with Don Ramirez on
computation of surface measures of ellipsoids in N-space via
Lauricella F_D functions and an application to optimal designs in
statistics.
Charles Dunkl
Topic #3 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: Hans Haubold
Subject: Al-Salam's ftp site transferred to Vienna
Dear Colleague,
The anonymous ftp site at
euler.math.ualberta.ca
has been transferred to the new anonymous ftp site at
unvie6.un.or.at, directory siam
starting on 19 September 1995.
The new ftp site can also be accessed by using a World Wide
Web browser ( Mosaic, Netscape, or their X Window
implementations) at the address ftp://unvie6.un.or.at/siam .
Manuscripts can be obtained from directory "siam/opfs" and
subdirectories. In particular, examine the file 00contents.ftpsite
in the "siam/submissions" directory.
You are invited to submit one or more of your not-yet-in-print
manuscripts which you wish to make available to the OPSF
community. They should be in TeX, LaTeX, AMSTeX, or AMSLaTeX
format. These manuscripts can be submitted by one of the
following methods:
a) anonymous ftp to unvie6.un.or.at
then "cd siam/submissions"
then "put file" where "file" is the name of the file you
wish to deposit
b) E-mail to haubold@ekpvs2.dnet.tuwien.ac.at
See Topic #20 for new additions to the archive.
Topic #4 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: Jim Goldman
Subject: Procedure for new subscribers to OP-SF Net
Beginning in October, SIAM will acknowledge via e-mail all new
subscriptions to activity group electronic newsletters. Previously, we
did not send such an acknowledgement, and the first response most
people received would have been the next issue of the electronic
newsletter to which they had subscribed. Depending on the publishing
frequency of the newsletter, a long wait between request and
acknowledgement sometimes resulted.
Topic #5 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: Stanislaw Zakrzewski
Subject: Minisemester on Quantum groups and quantum spaces
It was already announced in OP-SF Net 2.4, Topic #4 that the Stefan
Banach International Mathematical Center in Warsaw, Poland will host a
Minisemester on "Quantum Groups and Quantum Spaces" during November 6 -
December 1, 1995 and that the last week (November 27 - December 1)
will have the themes "Special Functions" and "Noncommutative Geometry
and Physics". A preliminary list of speakers for this week is now
available:
J.L. Azcarraga, B.L. Cerchiai, A. Connes, O.F. Dayi, M. Dijkhuizen,
L. Faddeev, G. Fiore, A.M. Gavrilik, K. Gawedzki, A. Kempf, M. Klimek,
A. Klimyk, E. Koelink, T. Koornwinder, A. Marlow, A. Odzijewicz,
J. Seifert, J. Stokman, K. Ueno, L. Vinet J. Wess
Further information:
WWW: http://info.fuw.edu.pl/~bqg95
or
ftp: ftp.fuw.edu.pl, directory pub/bqg95
or
email to the scientific secretary S. Zakrzewski
Topic #6 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: Walter Van Assche
Subject: 1-day conference Louvain-la-Neuve in honour of Professor Jean Meinguet
Special Topics in Numerical Analysis and Applied Mathematics
A 1-day conference in honour of Professor Jean Meinguet
December 1, 1995
Universite Catholique de Louvain,
room de La Vallee Poussin, Batiment de Hemptinne
Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve
The theme of the conference is the broad area of numerical analysis
and applied mathematics, but special emphasis will be put on the
following topics: approximation theory, matrix theory and scientific
computing. This one day conference is organized in honour of
Prof. Jean Meinguet of the Universite Catholique de Louvain, as an
acknowledgment of his leading role in these areas and in celebration
of his 65-th birthday.
Speakers:
Prof. Gene Golub, Stanford University,
Matrices, moments and quadrature
Prof. Herbert Stahl, Technische Fachhochschule Berlin,
Convergence domains for diagonal Pade approximants
Prof. Claude Brezinski, Univ. Sc. & Techn. Lille I,
Variations on Richardson's method and acceleration
Prof. Annie Cuyt, Universitaire Instellingen Antwerpen,
Convergence results for multivariate Pade approximants
Prof. Walter Gander, Eidg. Technische Hochschule Zurich,
Least squares problems in coordinate metrology
Prof. Walter Van Assche, Katholieke Universiteit Leuven.
Asymptotics for Freud polynomials and the information
entropies of the harmonic oscillator
There is no registration fee for the conference and the reception is
graciously offered by the Departement d'Ingenierie Mathematique (INMA).
For the banquet we request a booking before November 10. The banquet
fee is 950Bfr for a 3 course meal, wine included. You can transfer
this amount to the account mentioned on the registration form. After
November 10 the fee is raised to 1050Bfr. Late bookings are also
subject to approval by the restaurant and might be refused if too
numerous.
The conference will be held in room ``de La Vallee Poussin'', Cycl 01,
Batiment de Hemptinne, Chemin du Cyclotron, 2. Parking is available in
front of the building. For those coming from outside LLN we included a
map and travel directions. The reception will be held in the same
building.
The conference is organized by the Institut de Mathematique Pure et
Appliquee (MAPA), the Departement d'Ingenierie Mathematique (INMA),
and the Departement de Mathematique (MATH).
Organizing committee:
Y. Felix (UCL-Math), P. Toint (FUNDP-Math), M. Willem (UCL-MAPA),
P. Habets, A. Magnus and P. Van Dooren (UCL-INMA).
For further information, please contact
A. Magnus, (magnus@anma.ucl.ac.be, tel: +32-10-47.31.57) or
P. Van Dooren (vdooren@anma.ucl.ac.be, tel: +32-10-47.80.40)
The conference is sponsored by the Fonds National de la Recherche
Scientifique and the Ministere de l'Education, de la Recherche et de
la Formation.
Topic #7 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: Richard A. Zalik
Subject: Session on Computational Harmonic Analysis and Approximation Theory
Special Session on Computational Harmonic Analysis and Approximation Theory
to be held during the annual meeting of the American Mathematical Society,
Orlando, Florida, January 10 - 13, 1996.
Organizers: R. A. Zalik and N. K. Govil, Auburn University.
List of participants
A. Aldroubi (National Institutes of Health)
G. Anastassiou (Memphis)
L. Auslander (CUNY)
J. J. Benedetto (Maryland)
P. Borwein (Simon Fraser)
C. Cabrelli and U. Molter (Buenos Aires)
I. Daubechies (Princeton)
G. Davis (Dartmouth)
N. K. Govil and R. A. Zalik (Auburn)
K. Grochenig (Connecticut)
D. Healy (Dartmouth)
M. Ismail (USF)
M. A. Kon (Boston) and L. Raphael (Howard)
D. Lubinsky (Witwatersrand)
D. Maslen (Utrecht)
M. Z. Nashed (Delaware)
R. Mohapatra (Orlando)
T. E. Olson (Dartmouth)
D. Rockmore (Dartmouth)
G. Strang (MIT)
V. Strela (MIT)
R. Tolimieri (CUNY)
M. Taylor (National Center for Atmospheric Research)
D. Walnut (George Mason)
The talks will be given on Wednesday January 10 (morning and afternoon),
and on Thursday morning.
Further information:
WWW: http://www.ams.org/amsmtgs/1908_special.html
(to be reached via the AMS home page at http://e-math.ams.org)
Topic #8 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: Richard Askey
Subject: Joint summer reasearch conference on Random matrices etc.
The following joint summer research conference will be quite relevant
for the audience of OP-SF Net:
Subject: Random Matrices, statistical mechanics, and Painleve transcendents
Dates: June 23 to June 27, 1996
Location: Mount Holyoke College, South Hadley, Massachusetts, USA
Cochairs: Pavel Bleher and Alexander Its,
both of Indiana University-Purdue University at Indianapolis
The analysis of correlation functions for exactly solvable
quantum models and of the partition functions in the theory of random
matrices has gradually become an exciting new branch of mathematical
physics which has deep connections with both the classical theory of
special functions and orthogonal polynomials and the modern theory of
quantum groups and topological quantum field theory.
Further details: Notices AMS, November 1995, pp. 1454-1457 or
WWW: http://www.ams.org/committee/meetings/src.html
(to be reached via the AMS home page at http://e-math.ams.org)
People interested in attending should send the following information
to the Summer Research Conference Coordinator, Conferences Department,
American Mathematical Society, P.O. Box 6887, Providence, RI 02940, USA;
fax: +1-401-445 4140; e-mail wsd@ams.edu :
1. Title and dates of conference desired
2. Full name
3. Mailing address
4. Area code and phone number for office, home, and FAX
5. E-mail address
6. Scientific background relevant to the topic of the conference
7. Financial assistance requested (or indicate if support is not required)
Deadline for receipt of requests for information is March 1, 1996.
Topic #9 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: conference organizers
Subject: XXI. International Colloquium on Group Theoretical Methods in Physics
XXI. International Colloquium on Group Theoretical Methods in Physics
15-20 July 1996, Goslar, Germany
Within this Colloquium there will be a.o. a symposium on Quantum Groups
covering the following topics:
quantum groups and their representations, quantum spaces and
quantum symmetries, differential calculus on quantum spaces and
quantum groups, non-standard deformations, Yangians, braided
Hopf algebras, relations to noncommutative Geometry, q-analogues
of special functions and partial differential equations.
The Local Organizing Committee consists of H-D. Doebner,
W. Scherer and P. Kramer. For the quantum groups symposium V.K. Dobrev
is a co-organizer.
You can receive the first announcement of this Colloquium on request by
sending email to group21@pt.tu-clausthal.de .
Topic #10 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: Virginia Kiryakova
Subject: Workshop Transform Methods & Special Functions, II (1996)
The Second International Workshop "Transform Methods & Special
Functions", August 1996, Bulgaria was preliminarily announced in
OP-SF Net 2.4, Topic #7. The first announcement has appeared now.
It is available on request by sending email to Virginia Kiryakova
. From this we
quote the following information:
Dates: August 23 - 30, 1996
Location: Black Sea resort "Golden Sands" near Varna, Bulgaria
The Workshop will be devoted to the 100th Anniversary of the Bulgarian
mathematician Academician Nikola Obrechkoff (1986 - 1963). He has
left an enormous and valuable heritage of more than 250 papers and
several monographs and manuals in various topics: Analysis, Algebra,
Number Theory, Numerical Analysis, Summation of Divergent Series,
Probabilities & Statistics etc. New edition and translation of
Obrechkoff's selected papers are also planned.
Topics of the Workshop:
Integral Transforms, Special Functions, Series Expansions, Fractional
Calculus, Algebraical Analysis, Generalized Functions, Operational
Calculus, Univalent Functions; Applications of these topics to Complex
Analysis, Differential and Integral Equations.
Scientific programme: includes invited lectures and short
presentations. Proceedings of the Workshop will be published. The
requirements and the deadlines for the abstracts and papers will be
specified in the Second Announcement.
Registration Fees: USD 150 (or USD 130, if sent in advance, by January
15, 1996), for accompanying persons: USD 60. These fees are to cover
the necessary organization and administrative expenses of the
Workshop, the Abstracts and Proceedings "TM&SF'96", the social
programme (coffee breaks, excursion, welcome party) as well as the
local transport from / to Varna Airport (about 27 km).
The deadline for registration is 15 January 1996.
Topic #11 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: Walter Van Assche
Subject: Death of Joe L. Ullman
(This topic was borrowed from the OP-SF Newsletter, October 1995.
Look there for some more mathematical details and for references.)
Joe L. Ullman, Professor Emeritus of the University of Michigan, died
on Monday, September 11, 1995 at the age of 72. Ullman is known for
his work in logarithmic potential theory and orthogonal polynomials,
and he has made important contributions to the theory of orthogonal
polynomials on the infinite interval and Chebyshev quadrature (with
equal weights at every node). Joe was a student of Gabor Szego under
whose supervision he prepared his Ph.D. thesis on "Studies of Faber
polynomials" at Stanford University in 1949.
Ullman was born January 30, 1923 in Buffalo, New York. He received his
B.A. from the University of Buffalo in 1942. He fought in World War II,
receiving a purple heart, and later served as an instructor of
mathematics at army schools in Czechoslovakia and France. After his
Ph.D. he joined the faculty of the Department of Mathematics at the
University of Michigan, where he taught and did his research for 44
years.
Ullman's name will forever be connected with Ullman's criterion for
regular asymptotic behaviour of orthogonal polynomials and regular
zero behaviour. Ullman's criterion for orthogonal polynomials with
respect to a positive measure on [-1,1] is that the the minimal
carrier capacity of the measure is equal to the capacity of its
support, which is 1/2 if the support is [-1,1$. The asymptotic
distribution of the contracted zeros of Freud-type orthogonal
polynomials is given by a measure with explicit density which is
known as the Ullman measure in view of certain results of Ullman. He
also showed that equal weight quadrature (Chebyshev quadrature) is
possible on an infinite interval, which is a rather surprising result.
At home he was always ready to help his wife Barbara at their little
farm (with a dozen sheep and some goats), but most of us will
remember him for his love of classical analysis and his interesting
research, as can be judged from the following quote from the book by
Stahl and Totik: "It was especially J. Ullman who systematically
studied different bounds and asymptotics on orthogonal polynomials
with respect to arbitrary measures on [-1,1], and we owe a lot to his
research and personally to him for initiating and keeping alive the
subject".
Topic #12 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: Daniel W. Lozier
Subject: Software Testing Service for Special Functions
This is a project of Daniel W. Lozier. Its purpose is to begin to
develop software at the National Institute of Standards and Technology
for use in testing the accuracy, or numerical precision, of
mathematical software for special functions. The service would use the
World Wide Web to receive test requests and return test results. The
tests would be run on a network of workstations at the Institute. It
is hoped that the service will be of practical utility to anyone who
uses special functions in physics or other applications, and that it
will stimulate the interest of applied mathematicians who are
interested in computation of special functions as well as computer
scientists who are interested in innovative uses of the Internet.
References (Chronological Order)
[1] Numerical Evaluation of Special Functions, by D.W. Lozier and
F.W.J. Olver, gives a simple classification of special functions and a
cross-index to published algorithms and software for their numerical
evaluation. The original reference is W. Gautschi, Mathematics of
Computation 1943-1993: A Half-Century of Computational Mathematics,
American Mathematical Society Proceedings of Symposia in Applied
Mathematics 48 (1994), 79-125. It is presented in hypertext on WWW to
assist in locating information about specific special functions. See:
http://math.nist.gov/nesf/
[2] Software Needs in Special Functions, by D. W. Lozier, will appear
in the Journal of Computational and Applied Mathematics in 1996. A
preprint, NISTIR 5490, National Institute of Standards and Technology,
August 1994, is available from the author.
[3] Software Testing Service for Special Functions: A Proposal and
Request for Comments, by D.W. Lozier, provides details of the proposed
testing service and asks for comments on its feasibility and utility.
This document is an informal working paper that is not intended for
ordinary publication. Date: October 1995. See WWW:
http://math.nist.gov/stssf
The views of all interested individuals about this proposal are
sought. Comments on the feasibility, utility, or any other aspect of
the proposal can be sent to the author .
Topic #13 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: Steven Finch
Subject: Math Constants Web Resource
The Favorite Mathematical Constants web page
http://www.mathsoft.com/asolve/constant/constant.html
is an evolving collection of essays about constants, other
than pi and e, which appear throughout mathematics. Well-known
examples are due to Euler, Catalan, Khintchine and Feigenbaum,
but there are many others too.
The essays are accessible to advanced undergraduates and
intended to be starting points for continuing research (so
bibliographies are as complete as possible).
Please drop by and, of course, leave comments or suggestions
on how to improve these pages. I strongly recommend using
Netscape 1.1 or higher.
As a teaser, I offer the following:
Can the infinite product
(1^(1/1))*(3^(1/9))*(5^(1/25))*(7^(1/49))*(9^(1/81))* ...
be expressed in terms of known constants?
Steven Finch
sfinch@mathsoft.com
Topic #14 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: muldoon@mathstat.yorku.ca
Subject: Gatteschi Festschrift
The following books have appeared:
G. Allasia, ed., Special Functions, Annals of Numerical Mathematics
(ISSN 1021-2655; Claude Brezinski, Editor-in-Chief), vol. 2, Nos. 1-4,
Baltzer Science Publishers, Amsterdam, The Netherlands, 1995.
G. Allasia, ed., Special Functions, Numerical Algorithms, vol. 10,
Nos. 1-2, Baltzer Science Publishers, Amsterdam, The Netherlands, 1995.
These books contain the proceedings of an International Symposium on
Special Functions, held at the University of Torino in October 1993 on
the occasion of the 70th birthday of Luigi Gatteschi. The two volumes
include 11 invited lectures and 31 contributed papers by 66 authors
from many countries, for a grand total of over 700 pages.
The first volume opens with a brief Preface including an extract from
a letter by Richard Askey describing the connection between Torino and
Special Functions going back to the work of Lagrange continued in the
20th century by Tricomi and more recently by Gatteschi. This is
followed by a photograph of Gatteschi and a list of his publications.
Walter Gautschi's opening article "Luigi Gatteschi's work on special
functions and numerical analysis" goes beyond its title to include
some remarks of a biographical nature. Gatteschi's substantial
contribution to the subject of error terms in asymptotic
approximations of special functions is partially reviewed in Roderick
Wong's paper "Error bounds for asymptotic approximations of special
functions". Among the other more substantial invited papers are one
on the weights of positive quadrature formulas for ultraspherical
weight functions by K.-J. Forster and one on orthogonal polynomials on
weighted Sobolev spaces by F. Marcellan, T.E. Perez and M.A. Pinar.
Among the contributed papers in the first volume, those which caught
the eye of this reader were "Maximum principles and inequalities for
special functions" by D. Kershaw, "A monotonicity property of
ultraspherical Christoffel numbers" by J. Korevaar and "The Bieberbach
conjecture", a mainly expository paper with a conjecture on
bi-univalent functions, by H.V. Smith.
These volumes form a fitting tribute to Luigi Gatteschi; we are
indebted to Giampietro Allasia for making their publication possible.
The tables of contents of these volumes may be found on the World Wide Web:
http://www.NL.net/~baltzer/anuma.2.html
http://www.NL.net/~baltzer/numa.html
See also the home page of Baltzer Science Publishers:
http://www.NL.net/~baltzer/
or send email to publish@baltzer.nl
Topic #15 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: George Anastasiou
Subject: Special issue of Computers and Math. on Concrete Analysis
(shortened by OP-SF Net editor)
The journal "Computers and Mathematics witt Applications"
(editor in chief Ervin Y. Rodin) had a special issue on "Concrete Analysis"
(guest editor George A. Anastassiou):
Volume 30, Number 3-6, Sept. 1995.
While it is mainly dealing with approximation theory, it also
contains a few papers on orthogonal polynomials.
Topic #16 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: Tom H. Koornwinder
Subject: Impression from the Mittag-Leffler Institute, Sweden
During almost two months I am staying here at the Mittag-Leffler
Institute in Djursholm, Sweden. Djursholm is a suburb north of
Stockholm, with luxurious villas on big lots, and beautifully located
at the Stockholm archipelago. The institute is housed in the villa
which was built in 1890 for the Swedish mathematician G\"osta
Mittag-Leffler (1846-1927) and which was drastically reconstructed and
extended several times during the next fifteen years. Mittag-Leffler
and his Finnish wife Signe, nee Lindfors, lived here for the rest of
their life. The villa is towering on a hill and makes the impression
of a small castle. From the beginning the library took a central place
in the villa, and the whole architecture is a function of the
necessity to house a library which was the largest private mathematics
library in the world.
Mittag-Leffler is well-known by his work in function theory, but his
greatest merit for mathematics is probably in his extensive
international contacts with the top mathematicians of that time
and in his founding (in 1882) and editing of the journal Acta
Mathematica. From the beginning, first-rate contributions from
leading mathematicians in France, Germany and other countries were
obtained, and the journal is still considered as one of the highest
ranking mathematics journals in the world.
In 1916 Mittag-Leffler and his wife set up a foundation to promote
research in pure mathematics in the Scandinavian countries (see G. &
S. Mittag-Leffler, Testament 16/3 1916, Acta Math. 40 (1916), III-X.
The foundation was to maintain the large library in the villa and to
support a research institute there with several professors, and with
fellowships for younger mathematicians. In 1916 the plans for the
Institute were realistic at least in that Mittag-Leffler's financial
resources were adequate for the task. However, in 1922 there was a
large financial crash related to the economic crisis in Europe at the
time. The crash brought Mittag-Leffler near to bankruptcy and at his
death in 1927 the resources did not allow the realisation of his
original intentions.
The Royal Swedish Academy of Sciences, which had incorporated the
Institute in 1919, appointed Torsten Carleman as Director of the
Institute. Until 1969, the activities of the Institute were mainly
restricted to maintaining the library and editing Acta Mathematica.
From 1969 on outward funding was obtained by which the new director
Lennart Carleson could finally realise Mittag-Leffler's intentions.
From then on, a topic is chosen for every year. Within this field
experts are invited to work at the Institute for periods of one or
more months, and fellowships are made available for post-docs and
graduate students. When one looks at the list of programs of the past
twenty-five years, one sees topics from analysis dominating, while
algebraic geometry has also been repeatedly a topic of concentration.
The program for the present academic year is Analysis on Lie Groups.
The library is really marvellous, both as a piece of architecture and
because of its wealth of older books and journals. It also tries to
keep up with the present-day flood of books and journals, but it
succeeds of course only partially. Applied mathematics is not
represented very strongly. The library does not subscribe to any of
the SIAM journals, not even to the SIAM Journal on Mathematical
Analysis.
As for Acta Mathematica, it is very interesting to look at the "Table
generale des tomes 1-35" which was published in 1913. For this task
the young Marcel Riesz, coming from Hungary, was hired by Mittag-Leffler.
For all authors in alphabetical order one finds there a vitae and a
list of publications which appeared in Acta. There is a picture
gallery of the authors as well. Various well-known authors in
orthogonal polynomials and special functions can be found there, for
instance Thomas Stieltjes. In Volume 2 (1883) one already finds a
paper by E. Goursat "Sur une classe de fonctions representees par des
integrales definies", and in Volume 3 (1883) a short note by H. Mellin
"Eine Verallgemeinerung der Gleichung
$ \Gamma(1+x) \Gamma(1-x) = \pi x / \sin(\pi x) $". Also in the recently
published issue of Acta Mathematica special functions do occur in
E. Opdam's paper "Harmonic analysis for certain representations of graded
Hecke algebra", Acta Math. 175 (1995), 75-121. Although the outsider
would not guess this from the title, what really happens here is
generalizing the Plancherel formula and the Paley-Wiener theorem for
the Mehler-Fock transform to an integral kernel involving Jacobi
functions associated with an arbitrary root system (the so-called
Heckman-Opdam hypergeometric functions).
More information about the Mittag-Leffler Institute can be found
on WWW: http://www.ml.kva.se/ . In particular, see under General
Information a short account of the history of the Institute, from
which I borrowed for this article. On the occasion of the centennial
of Acta Mathematica two articles appeared in Acta Math. 148 (1982):
by Y. Domar, "On the foundation of Acta Mathematica" and by A. Weil,
"Mittag-Leffler as I remember him". Recently a book appeared on the
history of Swedish mathematics (in Swedish): Lars Garding,
"Matematik och Matematiker. Matematik i Sverige f\"ore 1950", Lund
University Press, 1994. It contains a chapter on Mittag-Leffler.
Tom Koornwinder
Topic #17 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: George Gasper
Subject: New errata for the book Basic hypergeometric series
Errata, updates of the References, etc.,
(as of October 17, 1995) 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
are now available on file from
WWW: http://www.math.nwu.edu/preprints/gasper/bhserrata/index.html
Below are the errata added to the list since March 30, 1995:
p. 78, eq. (3.8.1): Replace the factor `` $p^k$ '' on the right side of the
summand by `` $p^{2 k}$ '' .
p. 88, eq. (3.10.5): Replace the `` $q^{n+1}$ '' in the argument of the series
by `` $q^{n-1}$ '' . The right side of the equation may be simplified to
`` $(-aq, aq^2/w, w/aq; \, q)_n / (-q, aq/w, w; \, q)_n$ '' .
p. 88, eq. (3.10.7): Replace `` $(-a q^2,$ '' on the right side of the
equation by `` $(-a q,$ '' .
p. 88, eq. (3.10.9): The right side of the equation may be simplified to
`` $(w/aq, -a^{1/2}, aq^2/w; \, q)_n \over (w, -a^{-1/2},aq/w; \, q)_n$ '' .
p. 89, eq. (3.10.14): The fraction on the right side of the equation may be
simplified to `` $(-aq, aq^2/w, w/aq; \, q)_n \over (-q, aq/w, w;\, q)_n$''.
p. 137, Ex. 5.18 (iii): Add `` when $bcde = q^{n+1},$ '' .
p. 137, Ex. 5.18 (iv): Add `` when $bcde = q^{n+3},$ '' .
p. 240, eq. (II.37): Replace the first factor `` $(p; p)_n$ '' in
the denominator by `` $(p; p)_k$ '' .
p. 89: In the numerator of the display at the bottom of the page, replace
``$ -\lambda q^{n+1}$ '' by `` $-\lambda q^{n+1}/a$ '' .
p. 27, Ex. 1.32: Place a period at the end of the first sentence.
p. 73, eq. (3.6.19): Replace `` $q)_{n-1}$ '' by `` $p)_{n-1}$ '' .
p. 5, third paragraph: Replace each `` $b_s|$ '' by `` $b_s q|$ '' .
p. 88, eq. (3.10.8): Replace `` $, a/q^2;$ '' on the right side of the
equation
by `` $, a/q b^2;$ '' .
Topic #18 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: OP-SF Net editor
Subject: ftp and WWW addresses
A more comprehensive list of ftp and WWW addresses relevant for our field
is available at
ftp: ftp.fwi.uva.nl
directory: pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir
file: WWWaddresses
or at the home page of the Activity Group
WWW: http://www.math.yorku.ca/Who/Faculty/Muldoon/siamopsf/
under "List of WWW pages of interest to members"
This file will be regularly updated, and the changes will be mentioned
in OP-SF Net. Please mail corrections and additions for this list to
me .
Between September 7 and November 8, 1995 the following addresses
in the file WWWaddresses were changed or added:
Journals:
SIAM Journal on Mathematical Analysis:
WWW: http://www.siam.org/journals/sima/sima.html
Preprint archives:
hep-th (theoretical high energy physics):
email: hep-th@xxx.lanl.gov or hep-th@babbage.sissa.it
WWW: http://xxx.lanl.gov/archive/hep-th
q-alg (quantum algebra including knot theory):
email: q-alg@eprints.math.duke.edu
WWW: http://www.msri.org:80/preprints/q-alg.html
Organisations:
SIAM Activity Group on Orthogonal Polynomials and Special Functions:
WWW: http://www.math.yorku.ca/Who/Faculty/Muldoon/siamopsf/
Other information:
Math Constants Web Resource
WWW: http://www.mathsoft.com/asolve/constant/constant.html
Software Testing Service for Special Functions (D.W. Lozier)
WWW: http://math.nist.gov/stssf
Individuals:
Christian Krattenthaler:
WWW: http://radon.mat.univie.ac.at/People/kratt
Daniel W. Lozier
WWW: http://math.nist.gov/acmd/Staff/DLozier/
Topic #19 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: OP-SF Net editor
Subject: Changes of address
The phone numbers of SIAM have changed:
Society for Industrial and Applied Mathematics
3600 University City Science Center
Philadelphia, PA 19104-2688, USA
tel.: +1-215-382-9800, fax: +1-215-386-7999
Jan Felipe van Diejen mentioned that his department has moved to
a new building. His new address is:
Department of Mathematical Sciences
University of Tokyo
Komaba 3-8-1, Meguro-ku
Tokyo 153
Japan
Fax : +81-3-5465 7012
E-mail : diejen@ms.u-tokyo.ac.jp
Vadim Kuznetsov will stay in Montreal during the next few months:
Centre de recherches mathematiques, Universite de Montreal
C.P. 6128, succ. Centre-ville
Montreal (Quebec)
H3C 3J7 Canada
Fax : +1-514-343 2254
E-mail : kuznetso@crm.umontreal.ca
Topic #20 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: Hans Haubold
Subject: New additions to Haubold's preprint archive
See Topic #3 for the announcement of Hans Haubold's preprint archive.
One can approach the archive by anonymous ftp to unvie6.un.or.at,
directory siam, or at the WWW address ftp://unvie6.un.or.at/siam .
Between 1 August and 1 October, 1995, the following additions
were installed in the "siam/opsf" directory:
J.F. van Diejen, Self-dual Koornwinder-Mcdonald polynomials.
(see siam/opsf/diejen1.tex).
L. Lapointe and L. Vinet, Exact operator solution of the
Calogero-Sutherland model. (see siam/opsf/vinet2272.tex).
P.G.A. Floris and H.T. Koelink, A commuting q-analogue of the
addition formula for disk polynomials. (see siam/opsf/floris-
koelink.tex).
G. Gasper, Lecture notes for an introductory minicourse on q-
series. (see siam/opsf/gasper/gasper-qseries.tex).
Between 2 October and 6 November, 1995, the following
additions were deposited in the "siam/submissions" directory:
W. Van Assche, Compact Jacobi matrices: From Stieltjes to
Krein and M(a,b). (see siam/submissions/compact-jacobi.tex).
A.I. Aptekarev, V. Kaliaguine, and W. Van Assche, Criterion
for the resolvent set of nonsymmetric tridiagonal operators.
(see siam/submissions/resolvent.tex).
A. Ronveaux and W. Van Assche, Upward extension of the Jacobi
matrix for orthogonal polynomials. (see
siam/submissions/ronveaux-vanassche.tex).
F. Pinter and P. Nevai, Schur functions and orthogonal
polynomials on the unit circle. (see
siam/submissions/schur.dvi and siam/submissions/schur.ps).
L. Golinskii, P. Nevai, and W. Van Assche, Perturbation of
orthogonal polynomials on an arc of the unit circle. (see
siam/submissions/arc.dvi and siam/submissions/arc.ps).
G. Gasper, Errata, updates of the References, etc., (as of
October 17, 1995) 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/submissions/bhserrata_revised.tex).
D.P. Gupta and D.R. Masson, Contiguous relations, continued fractions
and orthogonality (see siam/submissions/Phi2.tex).
T.H. Koornwinder and A.L. Schwartz, Product formulas and associated
hypergroups for orthogonal polynomials on the simplex and on a
parabolic biangle (see abstract in siam/submissions/biangle.abstract).
J.V. Stokman and T.H. Koornwinder, Limit transitions for BC type
multivariable orthogonal polynomials (see abstract in
siam/submissions/BLpollimit.abstract).
Topic #21 --------------- OP-SF NET ---------------- November 9, 1995
~~~~~~~~~
From: OP-SF Net editor
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.fwi.uva.nl, in directory
pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir
or WWW:
ftp://ftp.fwi.uva.nl/pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir
Contributions to the OP-SF Net 3.1 should reach the email
address poly@siam.org before January 1, 1996.
The Activity Group also sponsors a Newsletter edited by Wolfram Koepf.
Deadline for submissions to be included in the February 1996 issue is
January 15, 1996. Please send your Newsletter contributions directly
to the Editor:
Wolfram Koepf
Konrad-Zuse-Zentrum
Heilbronner Str. 10,
D-10711 Berlin, Germany
tel.: +49-30-896 04-216
fax: +49-30-896 04-125,
email: koepf@zib-berlin.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.
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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