Volume 3, Number 5
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- September 12, 1996 -
- O P - S F N E T Volume 3, Number 5 -
- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -
- Editors: -
- Tom H. Koornwinder thk@fwi.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. Report on SIAG/OS events at the 1996 SIAM Annual Meeting
2. Publicity about OP-SF in SIAM News
3. First ISAAC Conference, Delaware, June 1997
4. CRM Workshop on Algebraic Combinatorics
5. Symposium on orthogonal polynomials in Seville
6. Death of M.P. Schutzenberger
7. Death of Carl Herz
8. Article on Szego by Askey & Nevai
9. Editorial board of SIAM J. Math. Anal.
10. Call for contributions to J. Phys. A
11. Report on Mini-conference on q-Series
12. Special issue of J. Symbolic Computation
13. (q)-Zeilberger algorithm
14. Question on Bessel polynomials in quantum mechanics
15. Changes of Address, WWW pages. etc.
16. Obtaining back issues of OP-SF Net and submitting contributions
to OP-SF Net and Newsletter
Calendar of events: see issue/topic:
1996
September 1 - October 25: MSRI program on Enumeration and partially
ordered sets 3.3 #5
September 23-28: III International Conference on Functional Analysis
and Approximation Theory (Italy) 3.1 #13
1997
January 13-24: Workshop on Special Functions & Differential Equations,
Madras 3.3 #6
March 17 - May 30: MSRI program on Symmetric functions and
representation theory 3.3 #5
May 22-24: Centenary Conference, including minisymposium on special
functions in Madison, Wisconsin 3.4 #5
June 2-6: First ISAAC Conference (International Society for Analysis,
its Applications and Computation) in Newark, Delaware 3.5 #3
June 9-20: CRM Workshop on Algebraic Combinatorics, Montreal 3.5 #4
June 24-28: Continued Fractions and Geometric Function Theory
(Trondheim, Norway) 3.2 #8
July 14-18: SIAM 45th Anniversary Meeting, Stanford, California
July 14-18: 9th International Conference on Formal Power Series
and Algebraic Combinatorics, Vienna, Austria 3.4 #7
September 22-26: VIII Simposium sobre Polinomios Ortogonales y
Aplicaciones, Seville, Spain 3.5 #5
Topic #1 --------------- OP-SF NET --------------- September 12, 1996
From: Willard Miller, Jr. <miller@ima.umn.edu>
Subject: Report on SIAG/OS events at the 1996 SIAM Annual Meeting
SIAG/OS sponsored a minisymposium on Modern Topics in Orthogonal Systems
on Tuesday July 23, at the July 22-26,1996 SIAM Annual Meeting in Kansas
City, Missouri. Due to a cancellation by Robert Gustafson, only one major
topic was covered: Wavelets. There were three talks.
Gilbert Walter organized the session and led off with "Improving wavelet
approximations." Although discrete wavelets generally have superior
convergence properties compared to classical orthogonal systems, they
share the Gibbs' phenomenon shortcoming - which causes errors at the edge
of a truncated signal or image. It was shown by Shim and Volkmer that
this always happens for orthogonal approximations for all continuous
wavelets with sufficient decay. Walter presented ways of avoiding this
shortcoming for wavelets.
Peter R. Massopust spoke on "Multiwavelets, Multiresolution Schemes, and
Hyperbolic Conservation Laws." He presented multiresolution schemes based
on multiwavelets. These schemes employ a combination of interpolation and
direct evaluation. He showed how such multiresolution schemes can be used
to obtain accurate and computationally efficient numerical weak solutions
of partial differential equations arising in computational fluid dynamics.
Truong Nguyen spoke on "Image Coding Using Shift-Invariant Dyadic Wavelet
Transform", joint work with Y. Hui and C.W. Kok. He proposed a new class
of wavelet filters, shift-invariant wavelet filters, for the purpose of
image compression. The proposed shift-invariant wavelet transform has
better shift-invariant properties compared with the conventional dyadic
wavelet transform, without changing the structure. He proposed and
evaluated two bit allocation schemes, suitable for the proposed
shift-invariant wavelet transform coding, and presented experimental
results showing that the shift-invariant wavelet transform has better
energy compaction properties in image coding than the conventional wavelet
transform.
Later in the morning Carl de Boor gave the John von Neumann Lecture on
(multivariate) "Polynomial Interpolation." This was one of the highlights
of the meeting.
Two of the SIAG-OS officers, Martin Muldoon and Willard Miller,
participated in the week's events and held an impromptu business meeting
to discuss possible minisymposium topics for the SIAG-OS at the 1997 SIAM
Annual Meeting (July 14-18, Stanford University). The 1997 meeting themes
most relevant to our group are 1) Optimization and linear algebra, and 2)
Computer science applicable to large-scale scientific computing (including
visualization, and the impact of the World Wide Web. Among the ideas
discussed by your ever vigilant officers was a minisymposium of expository
talks on orthogonal polynomials with heavy emphasis on the use of symbolic
computation and links to online data bases as an aid to research. An
associated session of research talks on the same topics was also proposed.
A related idea is a session on handbooks (in a generalized sense, to
include the World Wide Web). A session of expository or research talks
related to Szego's work was suggested, appropriate since he was on the
Stanford faculty. Another possibility is a session on Orthogonal
Polynomials in Signal Processing. In general, Muldoon and Miller thought
that a session of expository rather than research talks would be most
useful to our membership, though more difficult to organize. They would
greatly appreciate suggestions and advice from the SIAG-OS membership. A
decision on the minisymposium topic or topics must be reached by late
October 1996, for submission to the meeting organizers.
Topic #2 --------------- OP-SF NET --------------- September 12, 1996
From: Martin Muldoon <muldoon@mathstat.yorku.ca>
Subject: Publicity about OP-SF in SIAM News
I had a conversation with Gail Corbett, Editor of SIAM News, during the
SIAM meeting in Kansas City. Gail welcomes material from us as from all
the Activity Groups.
But not all items from our own media are suitable for SIAM News. In
particular, announcements or reports of our own minisymposia are not
suitable unless there is something very special about them. These would
include important advances in the field, profiles of people, etc. Events
surrounding a birthday or anniversary might be suitable especially if they
involved a personality or event of interest to several groups.
Expository material is of interest. Basic material that would be
"well-known" to members of our own group would be suitable. Graphics and
other visual materials are specially welcoms. If somebody has written
something with a different audience in mind, the Editor would be pleased
to indicate how it should be changed to make it suitable for SIAM News.
I agreed to pass on the suggestion that we compile and send to Gail lists
of suitable topics and people. Even very tentative suggestions are
welcome. There are times when a suggestion might match a similar
suggestion from another source and then Gail would be more likely to
follow it up. When we send suggestions we need not be sure that the
suggested authors would be willing.
Topic #3 --------------- OP-SF NET --------------- September 12, 1996
From: Wolfram Koepf <koepf@zib.de>
Subject: First ISAAC Conference, Delaware, June 1997
In addition to the announcement in OP-SF Net 3.4, Topic #6, we give
here a more detailed announcement.
First ISAAC Conference. University of Delaware, Newark, Delaware,
June 2-6, 1997
ISAAC is an abbreviation for The International Society for Analysis,
its Applications and Computation. Analysis is understood here in the
broadest sense, including differential equations, integral equations,
functional analysis, and function theory. The first Congress of this
newly constituted society will be held at the University of Delaware,
between June 2 and June 6, 1997, at the Clayton Hall Conference Center
of the University of Delaware. The Conference Secretary is
Pam Irwin
Department of Mathematics
University of Delaware
email: irwin@math.udel.edu
Session 13 of this conference will be devoted to Orthogonal Polynomials,
organized by Wolfram Koepf. The emphasis of this session will be on the
use of symbolic computation in connection with orthogonal polynomials and
special functions. Symbolic computation has the potential to change the
daily work of everybody who uses orthogonal polynomials or special
functions in research or applications. It is the purpose of the proposed
section to bring together developers of symbolic algorithms and
implementations which are connected with orthogonal polynomials and
special functions with users of computer algebra systems who need this
type of software. Even though the emphasis is on special functions and
computer algebra, any talk in which orthogonal polynomials are crucial is
welcome. The following have tentatively agreed to present a lecture in
this session:
Victor Adamchik: On Series Involving the Riemann Zeta
Function
Renato Alvarez-Nodarse: Algebraic and Spectral Properties of
Orthogonal Polynomials: A Computer Algebra Approach
Tewodros Amdeberhan: Computer Aided Proofs of a
Determinant Identity
Richard A. Askey: Some Problems on Orthogonal Polynomials
Yang Chen, Mourad Ismail: Asymptotics of the Largest Zeros of
Some Orthogonal Polynomials
Charles F. Dunkl: Using Maple to Explore Special Functions of
Several Variables
Wolfram Koepf, Dieter Schmersau: Algorithms for Classical
Orthogonal Polynomials
Tom H. Koornwinder, Rene Swarttouw: rec2ortho: An
Algorithm for Identifying Orthogonal Polynomials Given by
Their Three-Term Recurrence Relation as Special Functions
Kelly Roach: Maple and Orthogonal Polynomials
Andre Ronveaux: Recurrence Relations for Connecting
Coefficients Between Some Orthogonal Polynomials Families - A
Simple Algorithm (Mathematica)
Walter J. Van Assche:
Rafael Yanhez:
Doron Zeilberger: The Super-Holonomic Hierarchy
If you are interested in participating in this session, send a message to
koepf@zib.de
For further updated information see the URL's
http://www.zib-berlin.de/~bzfkoepf/isaac.html
http://www.math.udel.edu/isaac/conferen/congr97.htm
Topic #4 --------------- OP-SF NET --------------- September 12, 1996
From: Louis Pelletier <activites@crm.umontreal.ca>
Subject: CRM Workshop on Algebraic Combinatorics
The Centre de recherches mathematiques (Montreal, Canada) is hosting a
year-long program in combinatorics and group theory in 1996-1997. The year
will be organized around a certain number of workshops spread throughout
the year.
A Workshop on Algebraic Combinatorics will take place during June 9-20,
1997.
The purpose of the workshop is to study interactions between Algebraic
Combinatorics and Symmetric Functions, with a special emphasis on Descent
Algebras of Coxeter groups in relation to quasi-symmetric functions and
non-commutative symmetric functions, and on doubly parameterized
(Macdonald) (q,t)-symmetric functions, in relation to harmonics of
reflection groups.
Organizers:
F. Bergeron (UQAM), N. Bergeron (York), C. Reutenauer(UQAM)
Invited Speakers:
P. Diaconis (*), A. Garsia, I. Gessel, I. Goulden (*), M. Haiman,
I. G. Macdonald, C. Procesi, L. Solomon, R.P. Stanley, J.Y. Thibon
(*) To be confirmed
Those wishing to participate in the above activities are invited to write to:
Louis Pelletier
CRM, Universite de Montreal
C.P. 6128, Succ. centre-ville
Montreal (Quebec) Canada H3C 3J7
E-mail: activites@crm.umontreal.ca
Further information on WWW:
http://www.crm.umontreal.ca/Activites/Thematic_Year_96-97.html
Topic #5 --------------- OP-SF NET --------------- September 12, 1996
-From: Walter Van Assche <Walter.VanAssche@wis.kuleuven.ac.be>
-Subject: Symposium on orthogonal polynomials in Seville
-From September 22 to 26, 1997 there will be a conference on orthogonal
polynomials in Sevilla, Spain:
VIII Simposium sobre Polinomios Ortogonales y Aplicaciones
This will be at the Facultad de Matematicas of the Universidad de
Sevilla.
The 8SPOA is in the line of the Third International Symposium on
Orthogonal Polynomials and their Applications (Erice, Italy, 1990) and
the VII Simposium sobre polinomios ortogonales y Aplicaciones
(Granada, Spain, 1991). The roots of this Simposium are in the old
Spanish national meetings held during the last decade:
I Simposium: Logrono, March 1983
II Simposium: Jaca, June 1984
III Simposium: Segovia, June 1985
IV Simposium: Laredo, September 1987
V Simposium: Vigo, September 1988
VI Simposium: Gijon, June 1989
VII Simposium: Granada, September 1991
These were organized to connect and to exchange the knowledge of the
Spanish people who use orthogonal polynomials in any way or domain. Year
after year the number of non-Spanish scientists attending the symposia was
increasing and in Granada out of the 150 participants, only 40 were from
Spain.
The scientific committee consists of
Christian Berg (Copenhagen, Denmark)
Antonio J. Duran (Sevilla)
Jose J. Guadalupe (La Rioja)
Guillermo Lopez Lagomasino (La Habana, Cuba)
Francisco Marcellan (Leganes, Madrid)
Jesus Sanchez-Dehesa (Granada)
Walter Van Assche (Leuven, Belgium)
The scientific program will consist of plenary lectures and short
communications (20 minutes). In the autumn (September) we will give more
details about the program and the plenary speakers.
The cost of attendance is expected to be reasonable. The following
estimates are subject to change. We estimate the registration to be around
20.000 pesetas (1 US dollar = 120 pesetas), which includes admission to
the Simposium, the book of abstracts, the proceedings, a reception, and
participation in some social events. The price for lodging and meals will
be about 6.000 pesetas per person per day.
In order to keep discussions informal, the size of the Simposium must be
limited to about 100 invited participants. Owing to space limitations, it
may happen that we will not be able to accommodate all those interested in
attending. To be on the safe side, we have already reserved a number of
rooms in the comfortable University Residence Hernando Colon. To see if
our estimates are not too far off the mark, we would appreciate if you,
already at this early stage, could indicate your potential attendance. If
you are interested in being invited to participate or in receiving
subsequent circulars, please send a message to the organizers as soon as
possible, and in any case not later than October 31, 1996.
The Simposium will be held at the building of the Facultad de Matematicas
of the Universidad de Sevilla. Both the faculty and the residence are in
Reina Mercedes Campus, about 30 minutes walking distance from the old
center of the city and 15 minutes walking distance from Maria Luisa Park
(Espana and America Squares).
Access to Sevilla is easy. Sevilla lies on the high speed railroad (AVE)
southwards from Madrid (two and a half hours). There are highways from
Madrid and Barcelona and there is an international airport with several
flights daily to Madrid and Barcelona.
Mailing Address:
VIII SIMPOSIUM SOBRE POLINOMIOS ORTOGONALES Y APLICACIONES
Departamento Analisis Matematico
Facultad de Matematicas
Universidad de Sevilla
Aptdo. 1160
41080 Sevilla
fax: +34-5-4557972
Email: 8spoa@obelix.cica.es
We look forward to seeing you in Sevilla.
The organizing committee
Antonio J. Duran
Pedro Lopez Rodriguez (secretary)
Further information on WWW:
http://www.wis.kuleuven.ac.be/wis/applied/walter/sevilla.html
Topic #6 --------------- OP-SF NET --------------- September 12, 1996
From: Tom H. Koornwinder <thk@fwi.uva.nl>
Subject: Death of M.P. Schutzenberger
Professor Marco P. Sch\"utzenberger (Paris) died on 30 July 1996 at
the age of 75. He is well-known for his work in (algebraic)
combinatorics, which touches special functions. He had great influence
on Dominique Foata, Doron Zeilberger and others who are working on the
interface of combinatorics and special functions. He was the first who
published the q-binomial formula and the functional equation for q-exp
under the relation xy = qyx (C. R. Acad. Sci. Paris 236 (1953), 352-353).
Topic #7 --------------- OP-SF NET --------------- September 12, 1996
From: Tom H. Koornwinder <thk@fwi.uva.nl>
Subject: Death of Carl Herz
Carl S. Herz, Redpath Professor of Pure Mathematics at McGill University,
died on May 1, 1995 at the age of 65. His general area of research was
harmonic analysis in a wide sense. His paper "Bessel functions of matrix
argument", Annals of Math. 61 (1955), 474-523 was a pioneering paper in
the field of special functions in several variables associated with Lie
groups and with root systems.
See also the obituary "Carl Herz 1930-1995" in Notices AMS, July 1996,
which is partly reproduced from Canadian Math. Soc. Notes, December 1995.
Topic #8 --------------- OP-SF NET --------------- September 12, 1996
From: Tom H. Koornwinder <thk@fwi.uva.nl>
Subject: Article on Szego by Askey & Nevai
Richard Askey and Paul Nevai wrote a very readable article "Gabor Szeg\"o:
1895-1985" in the Summer 1996 issue of the Mathematical Intelligencer
(vol. 18, no. 3, pp. 10-22). Just one quotation:
He (Gabor Szego) said to me (Bob Osserman) something to the effect:
Don't you think it's somewhat fraudulent that we claim to teach people
how to become research mathematicians? That's like claiming you can
teach someone how to become a poet. All you can really do is show by
example how research in mathematics is done, and then they either can
do it themselves or they can't.
Topic #9 --------------- OP-SF NET --------------- September 12, 1996
From: The Editors
Subject: Editorial board of SIAM J. Math. Anal.
Charles Dunkl informs us that he has resigned from the editorial board
of SIAM Journal on Mathematical Analysis on August 29, 1996.
Topic #10 --------------- OP-SF NET --------------- September 12, 1996
From: Vadim B. Kuznetsov <vadim@amsta.leeds.ac.uk>
Subject: Call for contributions to J. Phys. A
Dear friends,
I would like to attract your attention to the fact that Journal of Physics
A is in favour of publishing Papers and Letters from the field of
Orthogonal Polynomials/Special functions. As an example, see below a (very
incomplete) collection of recent titles in fields close to the OP-SF one
and published in the first 16 volumes of this year.
You are encouraged to submit some of your MS's to the Journal of Physics
A. For information on submission visit the URL http://www.iop.org.
Regards, Vadim Kuznetsov (member of Editorial Board J. Phys. A)
--
Analytical treatment of the Green function singularity in integral equations
of scattering theory (L405-L412) (21 August 1996)
The measure of the orthogonal polynomials related to Fibonacci chains:
the periodic case (4169-4185) (21 July 1996)
Relativistic orthogonal polynomials are Jacobi polynomials (3199-3202)
(21 June 1996)
Fock - Bargmann representation of the distorted Heisenberg algebra (3281-3288)
(21 June 1996)
Separation of variables for the A2 Ruijsenaars model and a new integral
representation for the A2 Macdonald polynomials (2779-2804) (7 June 1996)
Affine Hecke algebra, Macdonald polynomials, and quantum many-body systems
(L281-L287) (7 June 1996)
A new result for Laguerre polynomials (L277-L279) (7 June 1996)
An operator approach to the construction of generating functions for products
of associated Laguerre polynomials (L263-L270) (21 May 1996)
On a one-parameter family of q-exponential functions (L223-L227) (21 May 1996)
Relativistic Calogero - Sutherland model: spin generalization, quantum affine
symmetry and dynamical correlation functions (L191-L198) (21 April 1996)
On the coherent states for the q-Hermite polynomials and related Fourier
transformation (1659-1664) (21 April 1996)
The dual Hahn q-polynomials in the lattice (...) and the q-algebras (...)
and (...) (1435-1451) (7 April 1996)
Special representations of (...) at the roots of unity (1201-1214)
(21 March 1996)
Ramanujan-type continuous measures for biorthogonal q-rational functions
(329-338) (21 January 1996)
Minimum uncertainty states for the quantum group and quantum Wigner
d-functions (427-435) (21 January 1996)
Transformation of certain generalized Kampé de Fériet functions
(357-363) (21 January 1996)
Generalization of Weierstrassian elliptic functions to (...) (L17-L22)
(7 January 1996)
Topic #11 --------------- OP-SF NET --------------- September 12, 1996
From: The Editors
Subject: Report on Mini-conference on q-Series
A Mini-conference on q-Series (Combinatorics, Classical Number Theory,
Special Functions), organized by Gaurav Bhatnagar and Stephen C. Milne,
took place at Ohio State University on June 20, 21 and 22, 1996.
Below, we list the speakers and their titles. Further information,
including abstracts, is available at the website:
http://www.math.ohio-state.edu/~gaurav/conference/conference.html
Richard Askey, The binomial theorem and extensions through 25 centuries
Richard Askey, How do special functions arise?
Bruce Berndt, The Rogers-Ramanujan Continued Fraction
Douglas Bowman, Analytic continuation of basic hypergeometric series and the
inversive closure
Heng Huat Chan, On Ramanujan's Cubic Transformation for
_2F_1(1/3,2/3;1;z)
Sheldon Degenhardt, Weighted Inversion Statistics and their Symmetry Groups
James Haglund, Rook Theory and Hypergeometric Series
Christian Krattenthaler, A new bijective proof of Stanley's hook-content
formula for semistandard tableaux
Christian Krattenthaler, Advanced determinant calculus
Verne Leininger, Expansions for (q)_{\infty}^{n^2-1} and basic
hypergeometric series in U(n)
Steve Milne, New infinite families of exact sums of squares formulas, Jacobi
elliptic functions, and Ramanujan's tau function
Michael Schlosser, Multidimensional matrix inversions and multiple basic
hypergeometric series.
Topic #12 --------------- OP-SF NET --------------- September 12, 1996
From: Wolfram Koepf <koepf@zib.de>
Subject: Special issue of J. Symbolic Computation
The following are the contents of a special issue of the Journal of
Symbolic Computation which contains the Proceedings of a workshop on
"Symbolic Computation in Combinatorics" held during September 21-24, 1993,
at Cornell University. Some of the articles are on hypergeometric
identities, and might be of interest to the members of our Activity Group.
Journal of Symbolic Computation
Vol. 20, Nos. 5 and 6, November / December 1995
Special Issue: Symbolic Computation in Combinatorics $Delta_1$
Volume Editors: Peter Paule, Volker Strehl
Foreword 483
Andrews, G. E., On a Conjecture of Peter Borwein 487
Delest, M., Dubernard, J. P., Dutour, I.,
Parallelogram Polyominoes and Corners 503
Garvan, F. G., Ramanujan's Theories of Elliptic
Functions to Alternative Bases - a Symbolic Excursion 517
Gessel, I. M., Finding Identities with the WZ Method 537
Labelle, G., Some Combinatorial Results First Found
Using Computer Algebra 567
Lisonek, P., Closed Forms for the Number of Polygon
Dissections 595
Pirastu, R. and Siegl, K., Parallel Computation and
Indefinite Summation: a Parallel MAPLE Application for
the Rational Case 603
Pirastu, R. and Strehl, V., Rational Summation and
Gosper-Petkovsek Representation 617
Takayama, N., An Algorithm for Finding Recurrence
Relations of Binomial Sums and its Complexity 637
Flajolet, P. and Salvy, B., Computer Algebra Libraries
for Combinatorial Structures 653
Paule, P. and Schorn, M., A Mathematica Version of
Zeilberger's Algorithm for Proving Binomial
Coefficient Identities 673
Zeilberger, D., Three Recitations on Holonomic
Systems and Hypergeometric Series 699
Strehl, V. and Wilf, H. S., Five Surprisingly Simple
Complexities 725
Wilf, H. S., The Computer-aided Discovery of a Theorem
about Young Tableaux 731
Krattenthaler, C., HYP and HYPQ 737
Nemes, I. and Petkovsek, M., RComp: A Mathematica
Package for Computing with Recursive Sequences 745
Stembridge, J. R., A Maple Package for Symmetric
Functions 755
Corrigenda 769
Topic #13 --------------- OP-SF NET --------------- September 12, 1996
From: Tom Koornwinder <thk@fwi.uva.nl>
Subject: (q)-Zeilberger algorithm
Below follows an update about implementations of the Zeilberger
algorithm and its q-analogue, and accompanying papers and books.
1. The most recent versions of Doron Zeilberger's own Maple implementations
(see OP-SF Net 1.1, Topic #14) are EKHAD and qEKHAD, obtainable by
anonymous ftp from
math.temple.edu, directory pub/zeilberg/programs
or via Doron's home page
http://www.math.temple.edu/~zeilberg
An accompanying book, in fact covering much more appeared this summer:
M. Petkovsek, H.S. Wilf & D. Zeilberger,
A=B,
A.K. Peters, 1996.
2. Tom Koornwinder's Maple implementations zeilb and qzeilb
(see OP-SF Net 1.1, Topic #14) dating back
from 1992 have just been slightly revised and adapted to Maple V, Release 4.
They are obtainable by anonymous ftp from
ftp.fwi.uva.nl, directory
pub/mathematics/reports/Analysis/koornwinder/zeilbalgo.dir
or via Tom's home page
http://turing.fwi.uva.nl/~thk/
The accompanying paper
T.H. Koornwinder,
On Zeilberger's algorithm and its q-analogue,
J. Comput. Appl. Math. 48 (1993), 91-111
has been adapted accordingly. The slightly revised version, with title
"On Zeilberger's algorithm and its $q$-analogue: a rigorous description"
is also available from the ftp site just mentioned.
3. Wolfram Koepf implemented Zeilberger's algorithm and certain extensions
in Maple V, Release 4. (See OP-SF Net 1.9, Topic #5 for an earlier
implementation by him in 1994.) The present implementation is part of the
official distribution of Maple V, Release 4. It can be made operational by
the two commands
> with(sumtools):
> readlib(`sum/simpcomb`):
possibly followed, to get help, by
> ?sumtools
The accompanying paper is:
W. Koepf,
Algorithm for m-fold hypergeometric summation,
J. Symb. Comput. 20 (1995), 399-417.
Wolfram Koepf also wrote a book manuscript about these topics:
W. Koepf,
Algorithmic Summation and Special Function Identities with Maple,
To appear.
The new package "code", to be used for the generation of recurrence and
differential equations for sums and integrals, written in connection with
this book can be obtained from his home page
http://www.zib.de/koepf/
4. Peter Paule and M. Schorn implemented Zeilberger's algorithm
in Mathematica (see OP-SF Net 1.3, Topic #10), while Peter Paule
and Axel Riese similarly implemented the q-Zeilberger algorithm.
These implementations are available on
email request to Peter Paule <ppaule@risc.uni-linz.ac.at>.
The accompanying papers are:
P. Paule & M. Schorn,
A Mathematica version of Zeilberger's algorithm for proving
binomial coefficient identities,
J. Symb. Comput. 20 (1995), 673-698.
P. Paule & A. Riese,
A Mathematica $q$-analogue of Zeilberger's algorithm based on an
algebraically motivated approach to $q$-hypergeometric telescoping,
to appear in
"Special Functions, q-Series and Related Topics".
The Fields Institute Communications Series.
5. Rene Swarttouw used Koepf's Maple implementations of the Zeilberger
algorithm for an interactive package on World Wide Web for calculating
formulas for orthogonal polynomials belonging to the Askey-scheme.
See WWW:
http://www.can.nl/~demo/CAOP/CAOP.html
You can also approach this via Rene's home page
http://star.cs.vu.nl/~rene/
Topic #14 --------------- OP-SF NET --------------- September 12, 1996
From: Brian Williams <williams@mail.bucknell.edu>
Subject: Question on Bessel polynomials in quantum mechanics
For some time now, I have been attempting to find exactly solvable 1-D
quantum mechanical potentials by starting with the second order
differential equations solved by orthogonal polynomials and special
functions, and through relatively simple variable transformations,
converting these to differential equations that match the Schrodinger
form. I have recently been exploring Bessel polynomials, and I seem to be
finding that for these polynomials, it appears possible to generate
eigenfunctions solving a particular Schrodinger form, which have the
unique property that on the positive real axes (corresponding to a radial
type problem), they have no nodes or argument values where they equal
zero. The eigenfunction solutions appear to be square integrable,
although I have not imposed boundary conditions per se. My question is,
can these be valid quantum mechanical wavefunctions, or can these
eigenfunctions be used to generate valid quantum mechanical wavefunctions?
If they have no nodes, the original eigenfunctions could not be mutually
orthogonal, and yet this seems to be a standard requirement of quantum
mechanics, at least as I usually see it dealt with. It has been suggested
to me that what I am running into is an example of a "singular
Hamiltonian", a term with which I am unfamiliar. Do any readers know
anything about this kind of situation or "singular Hamiltonians?" I would
appreciate any help or contacts you might be able to suggest.
Sincerely,
Brian Williams, Chemistry, Bucknell University
Topic #15 --------------- OP-SF NET --------------- September 12, 1996
From: The Editors <thk@fwi.uva.nl>, <muldoon@yorku.ca>
Subject: Changes of Address, WWW pages. etc.
(1) Jasper Stokman (Univ. of Amsterdam) has started a personal home page:
http://turing.fwi.uva.nl/~jasper/
(2) For a longer period, starting September 1, 1996, Mathijs Dijkhuizen
will work again at Kobe University, Japan:
Mathijs S. Dijkhuizen
Department of Mathematics, Faculty of Science,
Kobe University, Rokko, Kobe 657, Japan
TEL: +81-78-803 0506 (office) FAX: +81-78-803 0723 (univ.)
+81-78-803 0515 (secr.) +81-78-881 2552 (home)
+81-78-881 3851 (home)
email: msdz@math.s.kobe-u.ac.jp
http://www.math.s.kobe-u.ac.jp/HOME/dijkhuizen
(3) For a one-year period, starting July 1, 1996, Arno Kuijlaars
is working at Katholieke Universiteit Leuven, Belgium:
Arno B.J. Kuijlaars
Departement Wiskunde
Katholieke Universiteit Leuven
Celestijnenlaan 200 B
3001 Leuven
Belgium
email: arno%twi%wis@cc3.kuleuven.ac.be
(4) Vadim Zelenkov (International Sakharov Institute on Radioecology
(ISIR), Minsk, Belarus) informs us that he has a WWW page at:
http://gray.isir.minsk.by/users/zelenkov
His research on multiphoton excitation of multilevel systems by laser
radiation uses the integral transform including orthogonal polynomials to
solve the the dynamics equations.
(5)Wolfram Koepf got a new email address and new URL for his home page:
email: koepf@zib.de
URL: http://www.zib.de/koepf/
(6) Here are some additional home pages of individuals in the OP-SF
community:
- Victor Adamchik
http://www.wri.com/~victor/
- Tewodros Amdeberhan
http://www.math.temple.edu/~tewodros/
- Richard Askey
http://conley.math.wisc.edu/~askey/
- Steve Milne
http://www.math.ohio-state.edu/~milne/
Topic #16 --------------- OP-SF NET --------------- September 12, 1996
From: OP-SF Net editor <thk@fwi.uva.nl>
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
or WWW:
http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html
Contributions to the OP-SF Net 3.6 should reach the email
address poly@siam.org before November 1, 1996.
The Activity Group also sponsors a Newsletter edited by Wolfram Koepf.
Deadline for submissions to be included in the October 1996 issue is
September 15, 1996 and for the February 1997 issue it is January 15, 1997.
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.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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- The appointed officers are: -
- Wolfram Koepf, Newsletter editor -
- Martin Muldoon, Webmaster and OP-SF Net editor -
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