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September 15, 2001
O P - S F N E T Volume 8, Number 5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Editor:
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
Subscribe by mailing to: poly-request@siam.org
or to: listproc@nist.gov
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Today's Topics:
1. Nominations
2. Tel Aviv Workshop on Approximation Theory
3. Reports on OPSFA, Rome, 2001
4. Special Functions 2000 (Tempe) Proceedings
5. OPSFA Patras Proceedings
6. Indian book on "Selected Topics in Special Functions"
7. George Andrews Festschrift
8. Death of Leonard Carlitz
9. Question on Painleve II numerics
10. Preprints in xxx Archive
11. Changes of address, WWW pages, etc.
12. About the Activity Group
13. Submitting contributions to OP-SF NET and Newsletter
Calendar of Events:
2001
September 17-21: Summer School on Orthogonal Polynomials, Harmonic
Analysis, Approximation and Applications,
Inzell, Germany 8.3 #4
October 1-5: "Numerical Algorithms", Conference in Honor of Claude
Brezinski, Marrakesh, Morocco 7.3 #3
October 28 - November 2: Workshop on Mathematical Physics,
Porto-Novo, Benin 8.2 #6
2002
February 20-21: Workshop on Approximation Theory, Tel Aviv, Israel 8.5 #2
July 1-2: International Conference on Differential, Difference
Equations and their Applications. Patras, Greece 8.4 #3
July 8-12 - SIAM 50th Anniversary & Annual Meeting
Philadelphia, Pennsylvania, USA
http://www.siam.org/meetings/an02/
including an Activity Group minisymposium
July 22 - August 2: IMA Summer Program "Special Functions in the
Digital Age" Minneapolis, Minnesota, USA 8.2 #7
August 5-14: Workshop on Special Functions at FoCM'02, "Foundations of
Computational Mathematics" Minneapolis,
Minnesota, USA 8.1 #1
August 12-17, 2002: Summer school in Orthogonal Polynomials and
Special Functions, Leuven, Belgium 8.4 #4
Future plans:
There are plans to organize a summer school on Orthogonal Polynomials and
Special Functions in Portugal in July 2003 (July). (Contact person:
Amilcar Branquinho). This is in the series Inzell, 2001 (OP-SF NET 8.3,
Topic #3), and Leuven, 2002 (OP-SF NET 8.4, Topic #4). The coordinator of
the three summer schools is Erik Koelink (koelink@dutiaw4.twi.tudelft.nl).
These summer schools are part of our Activity Group's scientific program.
The scientific committee consists of Erik Koelink, Rupert Lasser, Amilcar
Branquinho, Paco Marcellan and Walter Van Assche.
Topic #1 ------------- OP-SF NET 8.5 ------------ September 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Nominations
SIAM has accepted the report of the nominating committee for the upcoming
election of officers of our Group, for the period January 1, 2002 to
December 31, 2004. The candidates are as follows:
Chair Daniel Lozier, National Institute for Standards oand
Technology
Vice Chair Charles Dunkl, University of Virginia
Walter Van Assche, Katholieke Universiteit Leuven
Secretary Peter Clarkson, University of Kent at Canterbury
Peter McCoy, US Naval Academy
Program Director Francisco (Paco) Marcellan, Universidad Carlos III de
Madrid
Candidates have been invited to submit biographies and statements and
SIAM will shortly send ballots to the members of the Activity Group.
Topic #2 ------------- OP-SF NET 8.5 ------------ September 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Tel Aviv Workshop on Approximation Theory
[From AT-NET BULLETIN NO. 106, 25.8.2001]
Workshop on Approximation Theory
Celebrating Dany Leviatan's 60th Birthday
February 20 - 21, 2002
Tel-Aviv
Information: http://www.math.tau.ac.il/~levin/ws2002.html
Organizing Committee: Nira Dyn, David Levin, Allan Pinkus
Topics: Abstract and Classical Approximation Theory; Orthogonal
Polynomials; Wavelets; Non-linear Approximation; Ridge Functions; Shape
Preserving Approximation.
Present List of International Participants: Bruce Chalmers (Riverside),
Albert Cohen (Paris VII), Wolfgang Dahmen (Aachen), Ron DeVore (South
Carolina), Zeev Ditzian (Edmonton), Manfred v. Golitschek (Wurzburg),
Viktor Konovalov (Kiev), Giuseppe Mastroianni (Potenza), Paul Nevai
(Ohio), Konstantin Oskolkov (South Carolina), Igor Shevchuk (Kiev), Jozsef
Szabados (Budapest), Vladimir Temlyakov (South Carolina).
Participation is by invitation only. People interested in attending
should contact one of the organizers.
Topic #3 ------------- OP-SF NET 8.5 ------------ September 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Reports on OPSFA, Rome, 2001
The Sixth International Symposium on Orthogonal Polynomials, Special Functions
and Applications (OPSFA) took place at Ostia, near Roma, Italy from 18 to 22
June, 2001. Here are reports on the symposium from Tom Koornwinder, Bill Connett
and Peter Clarkson.
Some impressions by Tom Koornwinder
This recent conference was the sixth (or by a different counting the ninth)
in a series of European meetings which started in Bar-Le-Duc, France, 1984.
The regular participants of these conferences are like relatives from a
large family, spread over Europe (or even the world), which come together
every two or three years for a joyful reunion. Serious family matters
certainly have to be discussed, but enough time should remain available for
lighter talk, for good eating and drinking and for having a lot of fun. The
cousins from Southern Europe, who are also most numerous, have in
particular excelled during this long period in being hosts to their family.
The site of the 2001 meeting was Rome, or rather Lido di Ostia, which is Rome
on the sea. Ostia is certainly less exciting than Rome (a good thing for
keeping participants at the lectures), but Rome is still close enough (a 30
minute train ride for only 1500 Lire) to make evening visits to the city by
participants or daytime visits by accompanying persons a good option. Everything,
lectures, meals and accommodation, took place in an excellent and pleasant hotel
in the middle of a large neighbourhood packed with modern apartment buildings of
moderate height. Town planners have given this neighbourhood a human aspect by
spreading shops (including many bars) all over the neighbourhood instead of
concentrating them in a shopping mall. The seaside was within 10 minutes walking
distance.
Those who were in, or passed through, Rome on the Sunday afternoon and
evening before the meeting, could give testimony of some one million people
in the streets celebrating the Italian championship of their local soccer
team Roma, after a decisive match against Parma held in the city that afternoon.
No hooligans here, no riots, no plundering, but young men with their girl
friends, and fathers and mothers with their children all happy together
about the success of their favourite club for which they had to wait so
many years. (Later I read in a Dutch newspaper that there were still some
disturbances and casualties.)
The conference had two plenary lectures every morning. Afterwards, at least
on a generic day, there were 7 contributed lectures in four parallel
sessions. The plenary lectures lasted 60 minutes including discussion, the
contributed lectures 30 minutes including discussion and possible change of
room. The plenary lectures were the following:
- A. Laforgia, M. Muldoon and P.D. Siafarikas, Commemoration of A. Elbert
- R. Askey, Solutions of some q-difference equations
- C. Dunkl, Special functions and generating functions associated with
reflection groups
- D. Sattinger, Multipeakons and the classical moment problem
- D. Stanton, Orthogonal polynomials and identities of Rogers-Ramanujan type
- S.K. Suslov, On Askey's conjecture
- N.M. Temme, Large parameter cases of the Gauss hypergeometric function,
in particular in connection with orthogonal polynomials
- W. Van Assche, Multiple orthogonal polynomials
Speakers in all these lectures gave excellent presentations. In the commemoration
of A. Elbert the three speakers gave a very worthy and impressive account of this
Hungarian mathematician as a person and as a scientist. As one of the speakers
said and made evident, his work was underestimated by the mathematical community.
I am regretting now that I have never been in personal contact with this
interesting mathematician, who died much too young.
While all plenary lectures were very interesting for me, I was in
particular impressed by the lectures by Sattinger and by Van Assche. David
Sattinger, coming from nonlinear pde's and integrable systems, talked
about a surprising application of the classical Stieltjes moment problem
and the related continued fraction expansion to peakon and antipeakon
solutions of the Camassa-Holm equation. The Camassa-Holm equation is a
nonlinear pde refining the KdV equation, more suitable for modelling fluid
flows in thin domains. It supports solutions, so-called peakons, that are
continuous but only piecewise analytic. Solutions with the peak downwards
are called antipeakons. During a peakon-antipeakon collision the slope
becomes infinite. Closed form of peakon-antipeakon solutions, asymptotic
behaviour and scattering shift can be obtained from the continued fraction
expansion and the corresponding orthogonal polynomials. A good reference
is R. Beals, D.H. Sattinger and J. Szmigielski, Multipeakons and the
classical moment problem, Advances in Math. 154 (2000), 229-257.
Walter Van Assche talked about multiple orthogonal polynomials. This
notion has its roots in the nineteenth century, from simultaneous rational
approximation, in particular Hermite-Pade approximation. The theory of
multiple orthogonal polynomials came up in the Eastern European literature
during the past ten or twenty years. Recently it has got a further impulse
by work of Van Assche and his collaborators. These polynomials occur in
two variants, type I and type II. Type II means for instance that a
polynomial P(x) of degree n_1+n_2+...+n_r is orthogonal to all polynomials
of degree less than n_j with respect to an weight function w_j(x) on an
interval Delta_j (j=1,...,r). One can define multiple analogues of the
classical orthogonal polynomials. In a remarkable result of Van Assche,
Geronimo and Kuijlaars the Fokas-Its-Kitaev Riemann-Hilbert problem
associated with a system of orthogonal polynomials has a generalization to
the multiple case. See "Riemann-Hilbert problems for multiple orthogonal
polynomials", to appear in "Special functions 2000: Current perspectives
and future directions", Kluwer, 2001; also downloadable from W. Van
Assche's homepage.
The contributed talks were of great variety, such that something could
be found to everybody's taste. Two contributed lectures struck me as
having deserved more emphasis by the organizers and a larger time slot. In
a brilliant 25-minute lecture Peter Clarkson gave a survey of properties
of the Painleve equations, restricting to Painleve II for the sake of
exposition. The Painleve equations may be seen as nonlinear analogues of
the classical special functions. Peter Clarkson is writing the chapter on
Painleve equations in the forthcoming NIST Digital Library of Mathematical
Functions (successor to the Handbook of Mathematical Functions by
Abramowitz and Stegun). Dan Lozier, managing editor of this DLMF project,
gave a very informative contributed lecture about the present status of
this large-scale enterprise, which will be of enormous importance for the
future of special functions usage.
A very remarkable social event was Music for Friends on Tuesday evening,
where Gino Palumbo of Universita Roma Tre, one of the conference
organizers, played piano works, partly joint with Enrico Tronci, composed
by himself during the years 1977-1987.
The organizers did a great job. Still a few critical remarks may be in
order. - The opening session was scheduled to last for one hour, but it
was finished after 15 minutes. I would have enjoyed to hear more from the
mouths of local rectors, deans and chairmen about the history of the three
Roman universities, about the number of mathematics students, about the
reason why most mathematics students in Italy are female, but most
mathematics professors are male, and whether the Museo della Matematica
housed in the Dipartimento di Matematica of Universita di Roma "la Sapienza",
and mentioned in the very comprehensive booklet Tesori di Roma, is meant as
something serious or as a kind of joke. - The topics of lectures (more so
for the contributed than for the invited lectures) remained somewhat
classical and traditional, with emphasis on one-variable theory and
analytic methods. Some more follow-up of fascinating developments about
which one could hear last year in Tempe, Arizona and some more spin-off of
things going on during last half year at the Newton Institute in
Cambridge, UK about symmetric functions and Macdonald polynomials might
have been appropriate. - A generic criticism of common practice in math
meetings is that transparencies are displayed too briefly, so that it is
impossible to take notes and to digest their full contents. During the plenary
lectures this effect might have been softened by bringing in a second projector.
At some meetings xerox copies of transparencies of plenary lectures are
distributed. A cheaper alternative might be to scan the transparencies and put
them on the web or hotel TV system. Next porno flashes on the TV's in the hotel
rooms might be replaced by flashes from the transparencies of the plenary
lectures. After paying 20000 Lire one might then get the full view of the lecture
contents on one's TV screen. - One more thing about the web. It would have been
nice if the full schedule would have been on the web some days before the
beginning of the meeting.
From: William Connett
Like a visitor to ancient Herculaneum in 79 A.D., who had come to
town for the very good theater, your reporter arrived in Rome on the eve
of the climactic game of the Italian Soccer cup completely unaware of the
real drama that was about to unfold, thinking only of polynomials, and the
opportunity to visit a few historical monuments (where is the Forum
anyway?) and to pay the proper obeisance to a number of Christian
monuments, St. John Lateran, St. Lawrence outside the walls, the Basilica
of Sts. Cosmos and Damian, etc., and perhaps to recite "Ode to Melancholy"
on the grave of "a Young English Poet", when like the eruption of
Vesuvius, the triumph (by the score 3-1) of AS Roma over Parma late that
Sunday afternoon (June 17), changed my world, and the pandemonium let
loose on the streets of Rome by the hundreds of thousands of hysterical
fans was the most memorable single event of the trip. I was staying in
Trastevere, and I will never forget the torrent of modern charioteers
cascading down the Lungotevere di Anguillara, singing, shouting, blowing
trumpets, waving enormous yellow and red flags from what were actually
very small motorbikes, crossing the Ponte Palatino, and pooling in the
center of Rome.
Little did I realize, that the pool of people meant that the trolley
lines could not run, and soon the bus lines could not run either, and my
euphoria changed to the grim realization that the only way to get to the
Porta San Paola, and the train to Lido di Ostia, was to tramp, carrying my
suitcase, some three miles from Monteverde to Piramide. I caught the last
train, and collapsed amid a throng of very tired and somewhat inebriated
supporters for the thirty minute ride out to the Hotel Satellite in Lido
di Ostia.
This was quite a dramatic beginning to the Sixth International
Symposium on Orthogonal Polynomials, Special Functions and Applications
(OPSFA-VI). In spite of a long evening of rumpus and ruction in the
streets, the some one hundred and fifty mathematicians appeared Monday
morning, for the opening ceremony of a very interesting meeting. There
were seven plenary lectures, ninety two more technical research seminars,
and an open problem session on the last day of the meeting. The following
is a very impressionistic overview of some of the highlights of the
scientific meeting. One of the topics in Dick Askey's talk which opened
the meeting, was the problem of finding bounds for the maximum values of
the polynomials in an orthogonal family. He reminded us of the argument
due to Sonine, I believe, for the Jacobi polynomials, that gives a bound
for the maximum value of each polynomial in the interval of support, and
suggested several ways that this argument might be generalized to other
orthogonal families. I was intrigued.
The scientific committee (de Bruin, Laforgia, Marcellan, Muldoon,
Ricci, and Siafarikas) are to be congratulated for their efforts to bring
speakers to these meetings who have found new and interesting uses for the
classical mathematics. The excellent talk of David Sattinger was a good
example of this. I am still not sure what a "multipeakon" might be, but
found his application of the classical moment problem to this problem in
fluid dynamics a delight. In another direction, I was also intrigued by
the improbable idea presented by Walter Van Assche, of considering a
family of polynomials to be orthogonal with respect to two different
measures. These ideas were later elaborated on by Els Coussement, and
Jonathen Coussement in research seminars.
I must give the prize for innovation to Franz Peherstorfer for his
very exciting talk on the distribution of the zeroes of polynomials that
are orthogonal with respect to a weight supported on disjoint intervals of
the real line. I have used a simple version of this problem for years as a
summer project for college students, and although they (and I) have
learned much from the experience, nothing I knew prepared me for the
complexity of the machinery from complex variables that he employed to
give a definitive resolution to this problem. Well done!
Nonlinear special functions are alive and well. The talk of Peter
Clarkson did an excellent job pulling together a number of facts about the
solutions to the six Painleve equations, including the nonlinear
recurrence relations (Baecklund transformations) for the solutions of
several of them. I think that there is much more to come here. I also
enjoyed the seminar of Mohammed Sifi who did some very nice harmonic
analysis showing that the action of a particular Dunkl operator could be
considered as a multiplier that satisfied the Hormander condition, and
therefore was bounded in L^p for a range of p. Multiplier operators first
got me interested in special functions, and it is nice to see new
approaches to these old questions.
The physical arrangements for the meeting were excellent. The hotel
was comfortable, the food quite good, and the location away from the
bustle of the center of Rome, but on the Tyrrhenian Sea, was perfect for a
scientific meeting. In the gathering twilight, groups of mathematicians
could be seen strolling along the beach, sampling the excellent gelato
and, as is there wont, filling napkins with illegible calculations.
Arrivederci, Roma!
From: Peter Clarkson
The sixth International Symposium "Orthogonal Polynomials, Special
Functions and Applications" (OPSFA) was held in Rome, Italy, in June 201.
This was attended by about 150 scientists from around the world. The
plenary lectures were given by R. Askey, C.F. Dunkl, D. Sattinger, D.
Stanton, S.K. Suslov, N.M. Temme and W. van Assche. Further there was a
commemoration of A. Elbert by A. Laforgia, M. Muldoon and P.D. Siafarikas.
The contributed talks were given in four parallel sessions. The structure
of the meeting was similar to many others that I have attended. It was
extremely well organized. Locating the OPSFA meeting near to a city such
as Rome is certainly an additional attraction.
On a personal note that was the first OPSFA meeting which I have attended
and I enjoyed it very much (despite three hours delays for both my
London-Rome and Rome-London flights and missing luggage!). I had met a
number of the other participants previously at other meetings, in
particular the "Symmetries and Integrability of Difference Equations"
series of meetings (Esterel, Canada, 1994; Canterbury, UK, 1996; Sabaudia,
Italy, 1998; Tokyo, Japan 2000). My own research field is the study of
nonlinear differential equations and nonlinear difference equations, in
particular exact solutions and asymptotics. Frequently we use results from
"Special Functions" and "Orthogonal Polynomials", despite being linear
equations in the solution of the nonlinear problems. I was pleased and
encouraged that there were some talks on nonlinear problems at this
meeting, including a plenary lecture by David Sattinger.
I believe that there are many mathematicians and physicists who have
research interest in "Special Functions" and "Orthogonal Polynomials"
though not as their main field of research. I feel that the involvement of
such scientists in the OP-SF activity group and participation in future
OPSFA meetings should be strongly encouraged.
Topic #4 ------------- OP-SF NET 8.5 ------------ September 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Special Functions 2000 (Tempe) Proceedings
[From the web site:
http://www.wkap.nl/book.htm/0-7923-7120-8]
Special Functions 2000: Current Perspective and Future
Directions
Proceedings of the NATO Advanced Study Institute on Special
Functions 2000, held in Tempe, Arizona, USA
edited by
Joaquin Bustoz
Mourad E.H. Ismail
Sergei K. Suslov
NATO SCIENCE SERIES: II: Mathematics, Physics and Chemistry
Volume 30
The Advanced Study Institute brought together
researchers in the main areas of special functions and
applications to present recent developments in the theory,
review the accomplishments of past decades, and chart
directions for future research. Some of the topics covered
are orthogonal polynomials and special functions in one
and several variables, asymptotic, continued fractions,
applications to number theory, combinatorics and
mathematical physics, integrable systems, harmonic
analysis and quantum groups, Painlevé classification.
Contents and Contributors
- Preface.
- Foreword.
- Bailey's transform, lemma, chains and tree; G.E. Andrews.
- Riemann-Hilbert problems for multiple orthogonal polynomials;
W. Van Assche, et al.
- Flowers which we cannot yet see growing in Ramanujan's garden of
hypergeometric series, elliptic functions and q's;
B.C. Berndt.
- Orthogonal rational functions and continued fractions;
A. Bultheel, et al.
- Orthogonal polynomials and reflection groups; C.F Dunkl.
- The bispectral problem: an overview; F.A. Grunbaum.
- The Bochner-Krall problem: some new perspectives; L. Haine.
- Lectures on q-orthogonal polynomials; M.E.H. Ismail.
- The Askey-Wilson function transform scheme; E. Koelink, J.V.
Stokman.
- Arithmetic of the partition function; K. Ono.
- The associated classical orthogonal polynomials; M. Rahman.
- Special functions defined by analytic difference equations;
S.N.M. Ruijsenaars.
- The factorization method, self-similar potentials and quantum
algebras; V.P. Spiridonov.
- Generalized eigenvalue problem and a new family of rational
functions biorthogonal on elliptic grids; V.P.
Spiridonov, A.S. Zhedanov.
- Orthogonal polynomials and combinatorics; D. Stanton.
- Basic exponential functions on a q-quadratic grid; S.K. Suslov.
- Projection operator method for quantum groups; V.N. Tolstoy.
- Uniform asymptotic expansions; R. Wong.
- Exponential asymptotics; R. Wong.
- Index.
Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-7119-4
EUR 190.00 / USD 175.00 / GBP 120.00
Paperback, ISBN 0-7923-7120-8
September 2001, 536 pp.
EUR 80.00 / USD 74.00 / GBP 50.00
Topic #5 ------------- OP-SF NET 8.5 ------------ September 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: OPSFA Patras Proceedings
The Fifth International Symposium on Orthogonal Polynomials, Special Functions
and their Applications (OPSFA, for short), was held in Patras, Greece, September
20 - 24, 1999 (see OP-SF NET 7.1, Topic #8). The Symposium was dedicated to
Professor Ted Chihara in honour of his many contributions to the subject of
Orthogonal Polynomials. The Proceedings have now appeared as a volume of Journal
of Computational and Applied Mathematics, Volume 133, Issue 1-2, 1 August 2001,
edited by P.D. Siafarikas. Here is the table of contents from:
http://www.elsevier.com/locate/cam
Preface
xiii-xiv
List of talks presented at the conference
xv-xviii
List of registered participants
xix-xxvii
R. Askey, M.E.H. Ismail and W. Van Assche
Ted Chihara and his work on orthogonal
polynomials
1-11
T.S. Chihara
45 years of orthogonal polynomials: a view from
the wings
13-21
Jesus S. Dehesa, Andrei Martinez-Finkelshtein and Jorge
Sanchez-Ruiz
Quantum information entropies and orthogonal
polynomials
23-46
P. Deift, T. Kriecherbauer, K.T.-R. McLaughlin, S.
Venakides and X. Zhou
A Riemann-Hilbert approach to asymptotic
questions for orthogonal polynomials
47-63
A. Elbert
Some recent results on the zeros of Bessel functions
and orthogonal polynomials
65-83
W.N. Everitt, K.H. Kwon, L.L. Littlejohn and R. Wellman
Orthogonal polynomial solutions of linear ordinary
differential equations
85-109
Walter Gautschi
The use of rational functions in numerical
quadrature
111-126
A.B.J. Kuijlaars
Asymptotic analysis of the density of states in
random matrix models associated with a slowly
decaying weight
127-140
Manuel Alfaro, Juan J. Moreno-Balcazar, Teresa E.
Perez, Miguel A. Pinar and M. Luisa Rezola
Asymptotics of Sobolev orthogonal polynomials for
Hermite coherent pairs
141-150
I. Area, E. Godoy, A. Ronveaux and A. Zarzo
Solving connection and linearization problems
within the Askey scheme and its q-analogue via
inversion formulas
151-162
N.B. Backhouse
Resonant equations and special functions
163-169
D. Barrios Rolanía, G. Lopez Lagomasino and E.B. Saff
Asymptotics of orthogonal polynomials inside the
unit circle and Szego-Pade approximants
171-181
H. Bavinck
Differential operators having Sobolev-type
Laguerre polynomials as eigenfunctions: new
developments
183-193
S. Belmehdi
Generalized Gegenbauer orthogonal polynomials
195-205
Youssef Ben Cheikh
On some (n1)-symmetric linear functionals
207-218
Christian Berg and Henrik L. Pedersen
A completely monotone function related to the
Gamma function
219-230
E. Berriochoa, A. Cachafeiro and F. Marcellan
Differential properties for Sobolev orthogonality
on the unit circle
231-239
A. Bultheel, P. González-Vera, E. Hendriksen and O.
Njastad
Determinacy of a rational moment problem
241-252
Els Coussement and Walter Van Assche
Some properties of multiple orthogonal
polynomials associated with Macdonald functions
253-261
Azza Dachraoui
Weyl-Bessel transforms
263-276
S.B. Damelin, H.S. Jung and K.H. Kwon
A note on mean convergence of Lagrange
interpolation in Lp (0 < p \le 1)
277-282
G. Dassios and P. Vafeas
Connection formulae for differential
representations in Stokes flow
283-294
Marcel G. de Bruin and A. Sharma
Birkhoff interpolation on nonuniformly distributed
roots of unity II
295-303
J. de Graaf
Evolution equations for polynomials and rational
functions which are conformal on the unit disk
305-314
C. Diaz-Mendoza, P. Gonzalez-Vera and R. Orive
Pade approximants and quadratures related to
certain strong distributions
315-329
Dimitar K. Dimitrov
Connection coefficients and zeros of orthogonal
polynomials
331-340
Demosthenes Ellinas
Quantum diffusions and Appell systems
341-353
M. Foupouagnigni and A. Ronveaux
Fourth-order difference equation satisfied by the
co-recursive of q-classical orthogonal polynomials
355-365
Adelina Georgescu, Bogdan Nicolescu, Nicolae Popa and
Mircea Boloteanu
On special solutions of the Reynolds equation from
lubrication
367-372
Adelina Georgescu, Harry Vereecken, Holger Schwarze
and Uwe Jaekel
Classes of solutions for a nonlinear diffusion PDE
373-381
Jacek Gilewicz and Peter A. Shulimanov
A new lower bound for a rational approximation on
the positive real axis
383-385
C. Giordano and A. Laforgia
Inequalities and monotonicity properties for the
gamma function
387-396
F. Alberto Grunbaum
Electrostatic interpretation for the zeros of certain
polynomials and the Darboux process
397-412
E.K. Ifantis and P.N. Panagopoulos
Limit points of eigenvalues of truncated tridiagonal
operators
413-422
Katarzyna Kiepiela, Monika Pietrzyk and Jan Szynal
Meixner polynomials and nonvanishing
holomorphic functions
423-428
D.G. Kubayi
Bounds for weighted Lebesgue functions for
exponential weights
429-443
K.H. Kwon and D.W. Lee
Error estimates of Lagrange interpolation and
orthonormal expansions for Freud weights
445-454
A. Kyriakoussis and M.G. Vamvakari
Asymptotic normality of the coefficients of
polynomials associated with the Gegenbauer ones
455-463
Jean Letessier
Fourth-order difference equation for co-recursive
associated Meixner and Charlier polynomials
465-476
Andrei Martínez-Finkelshtein, Pedro Martínez-González
and Ramón Orive
On asymptotic zero distribution of Laguerre and
generalized Bessel polynomials with varying
parameters
477-487
M. Michalska and J. Szynal
A new bound for the Laguerre polynomials
489-493
Pierpaolo Natalini and Paolo Emilio Ricci
Computation of Newton sum rules for associated
and co-recursive classical orthogonal polynomials
495-505
Sotirios E. Notaris
Interpolatory quadrature formulae with Chebyshev
abscissae
507-517
Franz Peherstorfer
On Toda lattices and orthogonal polynomials
519-534
Vigdis Petersen
Modification of a method using Szego polynomials
in frequency analysis: the V-process
535-544
V.P. Plagianakos, N.K. Nousis and M.N. Vrahatis
Locating and computing in parallel all the simple
roots of special functions using PVM
545-554
Denys Pommeret
K terms recurrence relations and polynomial
variance functions of the Kth degree
555-565
L. Rebillard and A. Ronveaux
Expansion of multivariate polynomials in products
of univariate orthogonal polynomials: discrete
case
567-578
Jorge Sanchez-Ruiz and Jesus S. Dehesa
Some connection and linearization problems for
polynomials in and beyond the Askey scheme
579-591
Wim Schoutens
An application in stochastics of the Laguerre-type
polynomials
593-600
L.K. Stergioulas, V.S. Vassiliadis and A. Vourdas
Optimal bases of Gaussians in a Hilbert space:
applications in mathematical signal analysis
601-609
Franciszek Hugon Szafraniec
On matrix integration of matrix polynomials
611-621
N.M. Temme and J.L. Lopez
The Askey scheme for hypergeometric orthogonal
polynomials viewed from asymptotic analysis
623-633
P. Van Gucht and A. Bultheel
Bernstein equiconvergence and Fejér-type
theorems for general rational Fourier series
635-645
Luc Vinet, Oksana Yermolayeva and Alexei Zhedanov
A method to study the Krall and q-Krall
polynomials
647-656
A. Vourdas
Quantum systems with finite Hilbert space and
Chebyshev polynomials
657-664
A. Wuensche Hermite and Laguerre 2D polynomials
665-678
Martin Muldoon (editor)
Open problems. Contributions from
T.S. Chihara (two),
A. Elbert and A. Laforgia,
A. Elbert, A. Laforgia and P. Siafarikas,
D. K. Dimitrov,
J. Gilewicz,
E.K. Ifantis,
A. Kuijlaars,
G. Lopez Lagomasino,
W. Mlotkowski,
A. Ronveaux,
P.D. Siafarikas,
W. Van Assche,
A. Wuensche 679-701
Topic #6 ------------- OP-SF NET 8.5 ------------ September 15, 2001
~~~~~~~~~~~~~
From: Walter Van Assche
Subject: Indian book on "Selected Topics in Special Functions"
Selected Topics in Special Functions (R.P. Agarwal, H.L. Manocha,
K. Srinivasa Rao, eds.), Allied Publishers, New Delhi, 2001, vii+322 pp.
(ISBN 81-7764-169-7)
The Indian Society for Special Functions and their Applications (SSFA)
have asked some of their expert members to prepare a contribution for this
volume of selected papers. The editors hope that the book will be a
significant contribution of the Society and that it would motivate the
younger generation of mathematicians. They also hope that this volume,
with contributions made by a representative section of India, will have
some impact on the community of mathematicians all over the world. The
contributions are
R.P. Agarwal: Recent developments in the theory of
generalized hypergeometric series
H.L. Manocha: Lie theory, q-difference calculus and
q-functions
S. Bhargava: Cubic theta functions
A. Verma: Polybasic hypergeometric series
K. Srinivasa Rao: Hypergeometric series and quantum
theory of angular momentum
A.K. Agarwal: Some applications of special functions in
number theory and combinatorics
M.A. Pathan: Lie theory and generalized Bessel functions
R.Y. Denis and S.N. Singh: Generalized hypergeometric
functions and continued fractions
C. Adiga and D.D. Somashekara: Rogers-Ramanujan identities,
continued fractions and their generalizations
R.S. Pathak: Special functions and distributions
Vivek Sahai: Euler integral transformation, its
$q$-analogue and special functions using Lie theory and quantum theory
P.K. Banerji: Fractional differintegrals
R.K. Saxena: On the unification and extension of univariate
and bivariate distributions associated with special functions
C.M. Joshi: Exact asymptotic coefficients and bounds of
generalized hypergeometric functions
Topic #7 ------------- OP-SF NET 8.5 ------------ September 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: George Andrews Festschrift
[From the Springer web site: http://www.springer-ny.com]
THE ANDREWS FESTSCHRIFT
Edited by Dominique Foata
Price: $84.95
400 pages paperback
ISBN: 3-540-41491-6, published 2001
ABOUT THIS BOOK
This book contains seventeen contributions made to George Andrews on the
occasion of his sixtieth birthday, ranging from classical number theory
(the theory of partitions) to classical and algebraic combinatorics. Most
of the papers were read at the 42nd session of the Séminaire Lotharingien
de Combinatoire that took place at Maratea, Basilicata, in August 1998.
This volume contains a long memoir on Ramanujan's Unpublished
Manuscript and the Tau functions studied with a contemporary eye, together
with several papers dealing with the theory of partitions. There is also
a description of a maple package to deal with general q-calculus. More
subjects on algebraic combinatorics are developed, especially the theory
of Kostka polynomials, the ice square model, the combinatorial theory of
classical numbers, a new approach to determinant calculus.
TABLE OF CONTENTS
Dominique Foata, Guo-Niu Han: Introduction
George E. Andrews: Some Debts I Owe
Richard Askey: The Work of George Andrews: A Madison Perspective
Bruce C. Berndt, Ken Ono: Ramanujan's Unpublished Manuscript on the
Partition and Tau Functions with Proofs and Commentary
Frank Garvan: Q-series maple tutorial: A q-product tutorial for a q-series
maple package
G.-N. Han, A. Randrianarivony, J. Zeng: Un autre q-analogue des nombres
d'Euler
Michael D. Hirschhorn: Three classical results on representations of a
number
Dongsu Kim, Dennis Stanton: Simultaneous maj statistics
David P. Little: An extension of Franklin's Bijection
George E. Andrews, Peter Paule: MacMahon's Partition Analysis IV:
Hypergeometric Multisums
Anatol N. Kirillov, Anne Schilling, Mark Shimozono: Various representations of
the generalized Kostka polynomials
Herbert S. Wilf: The number-theoretic content of the Jacobi triple
product identity
Arturo Carpi, Aldo de Luca: Words and Repeated Factors
Adriano Garsia, Mark Haiman, Glenn Tesler: Explicit Plethystic Formulas
for Macdonald q,t-Kostka Coefficients
S. Ole Warnaar: Supernomial coefficients, Bailey's lemma and
Rogers-Ramanujan-type identities. A survey of results and
open problems
D. Foata, G.-N. Han: The triple, quintuple and septuple product
identities revisited
A. Lascoux: Square-ice enumeration
Christian Krattenthaler: Advanced Determinant Calculus
Topic #8 ------------- OP-SF NET 8.5 ------------ September 15, 2001
~~~~~~~~~~~~~
From: OPSF NET Editor
Subject: Death of Leonard Carlitz
Thanks to Tom Koornwinder for pointing out that the July 2001 issue of the
Notices of the American Mathematical Society mentioned that Leonard Carlitz died
in 1999 and that MathSciNet refers to obituaries by F. T. Howard in Fibonacci
Quart. 38 (2000), no. 4, 316, and by Joel V. Brawley in Finite Fields Appl. 6
(2000), no. 3, 203-206.
Topic #9 ------------- OP-SF NET 8.5 ------------ September 15, 2001
~~~~~~~~~~~~~
From: Steven Finch
Subject: Question on Painleve II numerics
[This appeared in opaftalk]
Here are four constants associated with the longest increasing subsequence
problem (Baik, Deift and Johansson):
mu=-1.77109, sigma=0.9018 (largest eigenvalue
of random GUE matrix)
mu'=3.6754, sigma'=0.7351 (second-largest e.v.)
of random GUE matrix)
http://front.math.ucdavis.edu/math.CO/9810105
http://front.math.ucdavis.edu/math.CO/9901118
These can be expressed as integrals involving a certain Painleve II ODE
solution that satisfies asymptotic boundary conditions.
The values came from Tracy and Widom:
http://front.math.ucdavis.edu/hep-th/9211141
who used asymptotic expansions of the Painleve II solution at both plus
and minus infinity to integrate forwards/backwards.
I am simply wondering if anyone has improved the estimates of these four
constants. Is Tracy-Widom's numerical analysis "state-of-the- art" for
this problem? Or can someone do better?
Thank you most kindly!
Steve Finch
MathSoft Engineering & Education, Inc.
101 Main St.
Cambridge, MA, USA 02142
http://www.mathsoft.com/asolve/sfinch.html
Topic #10 ------------- OP-SF NET 8.5 ------------ September 15, 2001
~~~~~~~~~~~~~
From: OPSF NET Editor
Subject: Preprints in xxx Archive
The following preprints related to the fields of orthogonal polynomials
and special functions were recently posted or cross-listed to one of the
subcategories of the xxx archives. See especially:
http://front.math.ucdavis.edu/math.CA
http://front.math.ucdavis.edu/math.CO
http://front.math.ucdavis.edu/math.QA
http://xxx.lanl.gov/archive/solv-int
math.CO/0107024
Title: Bijections behind the Ramanujan Polynomials
Authors: William Y. C. Chen, Victor J. W. Guo
Comments: 18 pages, 7 figures
Subj-class: Combinatorics
MSC-class: 11B83; 05C05
math.CA/0107036
Title: Spectral theory and special functions
Authors: Erik Koelink
Comments: Lecture notes for the SIAM Activity Group OP-SF summer
school 2000, Laredo, Spain. 40 page, latex
Subj-class: Classical Analysis
math.NT/0107043
Title: On the Divergence of the Rogers-Ramanujan Continued Fraction on the
Unit Circle
Authors: Jimmy McLaughlin, Doug Bowman
Comments: 25 pages
Subj-class: Number Theory
MSC-class: 11A55
math.RT/0107072
Title: The Strong Macdonald Conjecture
Authors: S. Fishel, I. Grojnowski, C. Teleman
Subj-class: Representation Theory; Combinatorics
MSC-class: 17B67; 17B55; 33C52
math.CA/0107082
Title: On some integrals involving the Hurwitz zeta function: part 2
Authors: Olivier R. Espinosa, Victor H. Moll
Comments: 17 pages, AMS-LaTeX
Subj-class: Classical Analysis; General Mathematics; Mathematical Physics
math.QA/0107126
Title: On the evaluation formula for Jack polynomials with prescribed
symmetry
Authors: P.J. Forrester, D.S. McAnally, Y. Nikoyalevsky
Comments: 18 pages
Subj-class: Quantum Algebra
math.CO/0107214
Title: q-Supernomial coefficients: From riggings to ribbons
Authors: Anne Schilling
Comments: 19 pages, svcon2e.sty file required
Subj-class: Combinatorics; Quantum Algebra
MSC-class: 11B65; 05E05; 82B23
math.QA/0107225
Title: Duality and self-duality for dynamical quantum groups
Authors: Hjalmar Rosengren
Comments: 26 pages
Subj-class: Quantum Algebra
MSC-class: 17B37, 20G42
cs.LG/0107033
Title: Yet another zeta function and learning
Authors: Igor Rivin
Subj-class: Learning; Discrete Mathematics; Probability Theory
ACM-class: I.2.6; G.3
math.RT/0108042
Title: Matrix Valued Spherical Functions Associated to the Complex
Projective Plane
Authors: F. A. Grunbaum, I. Pacharoni, J. Tirao
Comments: 70 pages, 1 figure
Subj-class: Representation Theory; Classical Analysis
MSC-class: 22E30; 22E46; 33C45
math.CO/0108043
Title: Restricted set of patterns, continued fractions, and Chebyshev
polynomials
Authors: T. Mansour
Comments: 9 pages
Subj-class: Combinatorics
MSC-class: 05A05; 05A15; 30B70; 42C05
math.NT/0108054
Title: On the exceptional zeros of Rankin-Selberg L-functions
Authors: Dinakar Ramakrishnan, Song Wang
Comments: 31 pages. For ps, dvi and pdf formats of the paper, see
http://www.math.caltech.edu/people/dinakar.html
Subj-class: Number Theory
MSC-class: 11F70; 11F66; 11F55; 11F80
math.CO/0108121
Title: Applications of the classical umbral calculus
Authors: Ira M. Gessel
Subj-class: Combinatorics; Number Theory
MSC-class: 05A40; 05A19, 05A10, 11B65, 11B68, 11B73
math.RT/0108185
Title: Dunkl operators for complex reflection groups
Authors: C. F. Dunkl, E. M. Opdam
Comments: 36 pages; Programme on Symmetric Functions and Macdonald
Polynomials at the Isaac Newton Institute
Subj-class: Representation Theory
MSC-class: 20F55 (Primary); 52C35, 05E05, 33C08 (Secondary)
math.CO/0108193
Title: Partial-sum analogues of the Rogers-Ramanujan identities
Authors: S. Ole Warnaar
Comments: 11 pages, AMS-LaTeX
Subj-class: Combinatorics; Quantum Algebra
MSC-class: Primary 05A19, 33D15; Secondary 05A17, 17B68
math-ph/0108019
Title: N-Level Quantum Systems and Legendre Functions
Authors: A. S. Mazurenko, V. A. Savva
Comments: 6 pages, latex, no figures, see also this http URL
Subj-class: Mathematical Physics
MSC-class: 34A05; 42C15
Journal-ref: Proceedings of Third Annual Seminar "Nonlinear phenomena
in complex systems", Minsk: Institute of Physics, 1995, 328
nlin.SI/0108049
Title: Duality, Biorthogonal Polynomials and Multi-Matrix Models
Authors: M. Bertola, B. Eynard, J. Harnad
Comments: Latex, 44 pages, 1 table
Subj-class: Exactly Solvable and Integrable Systems; Mathematical
Physics
nlin.SI/0107050
Title: On the Rational Solutions of q-Painlev\'e V Equation
Authors: Tetsu Masuda
Comments: 16 pages
Subj-class: Exactly Solvable and Integrable Systems
nlin.SI/0107062
Title: Relativistic Toda chain at root of unity II. Modified
Q-operator
Authors: S. Pakuliak, S. Sergeev
Comments: LaTeX2e, 27 pages
Subj-class: Exactly Solvable and Integrable Systems
nlin.SI/0107063
Title: Relativistic Toda chain at root of unity III. Relativistic Toda
chain hierarchy
Authors: S. Pakuliak, S. Sergeev
Comments: LaTeX2e, 21 pages, misprints corrected
Subj-class: Exactly Solvable and Integrable Systems
nlin.SI/0107074
Title: Transformations ${RS}_4^2(3)$ of the Ranks $\leq4$ and
Algebraic Solutions of the Sixth Painlev\'e Equation
Authors: F. V. Andreev, A. V. Kitaev
Comments: 26 pages
Subj-class: Exactly Solvable and Integrable Systems
nlin.SI/0108010
Title: Quasi-linear Stokes phenomenon for the second Painlev\'e
transcendent
Authors: A. R. Its (IUPUI, Indianapolis), A. A. Kapaev (PDMI, St
Petersburg)
Comments: 19 pages, LaTeX
Subj-class: Exactly Solvable and Integrable Systems
nlin.SI/0108052
Title: Asymptotics of semiclassical soliton ensembles: rigorous
justification of the WKB approximation
Authors: P. D. Miller
Comments: Submitted to Int. Math. Res. Not
Subj-class: Exactly Solvable and Integrable System
Topic #11 ------------- OP-SF NET 8.5 ------------ September 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Changes of address, WWW pages, etc.
AT-NET reports the following "Change of Coordinates" for Ed Saff
and for the editorial office for the journal Constructive Approximation:
E.B. Saff
Department of Mathematics
Vanderbilt University
Nashville, TN 37240
USA
email: esaff@math.vanderbilt.edu
phone: (615) 322-2014
fax: (615) 343-0215
Center for Constructive Approximation
Department of Mathematics
Vanderbilt University
Nashville, TN 37240
USA
email: ca@math.vanderbilt.edu
phone:(615) 343 4107
fax:(615) 343-0215
Ed Saff has a homepage at:
http://www.math.vanderbilt.edu/~esaff/
Topic #12 ------------- OP-SF NET 8.5 ------------ September 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: About the Activity Group
The SIAM Activity Group on Orthogonal Polynomials and Special Functions
consists of a broad set of mathematicians, both pure and applied. The
Group also includes engineers and scientists, students as well as experts.
We have around 140 members scattered about in more than 20 countries.
Whatever your specialty might be, we welcome your participation in this
classical, and yet modern, topic. Our WWW home page is:
http://math.nist.gov/opsf/
This is a convenient point of entry to all the services provided by the
Group. Our Webmaster is Bonita Saunders (bonita.saunders@nist.gov).
The Activity Group sponsors OP-SF NET, which is transmitted periodically
by SIAM. It is provided as a free public service; membership in SIAM is
not required. The OP-SF Net Editor is Martin Muldoon (muldoon@yorku.ca).
To receive the OP-SF NET, send your name and email address to
poly-request@siam.org.
Back issues can be obtained at the WWW addresses:
http://turing.wins.uva.nl/~thk/opsfnet
http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html
http://math.nist.gov/opsfnet/archive
The NET provides fast turnaround compared to the printed Newsletter, also
sponsored by the Activity Group, and edited by Renato Alvarez-Nodarse and
Rafael Yanez. It appears three times a year and is mailed by SIAM. Back
issues are accessible at:
http://www.mathematik.uni-kassel.de/~koepf/siam.html
To receive the Newsletter, you must be a member of SIAM and of the Activity
Group. SIAM has several categories of membership, including low-cost categories
for students and residents of developing countries. For current information on
SIAM and Activity Group membership, contact:
Society for Industrial and Applied Mathematics
3600 University City Science Center
Philadelphia, PA 19104-2688 USA
phone: +1-215-382-9800
email: service@siam.org
WWW : http://www.siam.org
http://www.siam.org/membership/outreachmem.htm
Finally, the Activity Group operates an email discussion group, called
OP-SF Talk. To subscribe, send the email message
subscribe opsftalk Your Name
to listproc@nist.gov. To contribute an item to the discussion, send
email to opsftalk@nist.gov. The archive of all messages is accessible
at:
http://math.nist.gov/opsftalk/archive
Topic #13 ------------- OP-SF NET 8.5 ------------ September 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Submitting contributions to OP-SF NET and Newsletter
To contribute a news item to OP-SF NET, send email to poly@siam.org with a
copy to the OP-SF Editor . Please note that submissions
to the Net are automatically considered for the Newsletter, and vice
versa, unless the contributor requests otherwise.
Contributions to OP-SF NET 8.6 should be sent by November 1, 2001.
Please send your (printed) Newsletter contributions directly to the Editors:
Renato Alvarez-Nodarse
Departamento de Analisis Matematico
Universidad de Sevilla
Apdo. Postal 1160,
Sevilla E-41080 Spain
fax: +34-95-455-7972
e-mail: renato@gandalf.ugr.es
ran@cica.es
Rafael J. Yanez
Departamento de Matematica Aplicada
Universidad de Granada
E-18071 Granada, Spain
phone: +34-58-242941
fax: +34-58-242862
e-mail: ryanez@ugr.es
preferably by email, and in latex format. Other formats are also acceptable and
can be submitted by email, regular mail or fax.
The deadline for submissions to be included in the February 2002 issue is
January 15, 2002. and for the June 2002 issue is May 15, 2002.
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OP-SF NET is a forum of the SIAM Activity Group on
Special Functions and Orthogonal Polynomials.
We disseminate your contributions on anything of interest to the
special functions and orthogonal polynomials community. This
includes announcements of conferences, forthcoming books, new
software, electronic archives, research questions, job openings.
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Get back issues from URL: http://turing.wins.uva.nl/~thk/opsfnet/
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The elected Officers of the Activity Group (1999-2001) are:
Daniel W. Lozier, Chair
Walter Van Assche, Vice Chair
Charles F. Dunkl, Secretary
Francisco Marcellan, Program Director
The appointed officers are:
Renato Alvarez-Nodarse and Rafael J. Yanez,
Newsletter Editors
Martin Muldoon, OP-SF NET editor
Bonita Saunders, Webmaster
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