Volume 5, Number 1
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- January 15, 1998 -
- O P - S F N E T Volume 5, Number 1 -
- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -
- Editors: -
- Tom H. Koornwinder thk@wins.uva.nl -
- Martin Muldoon muldoon@yorku.ca -
- -
- The Electronic News Net of the SIAM Activity Group -
- on Orthogonal Polynomials and Special Functions -
- -
- Please send contributions to: poly@siam.org -
- Subscribe by mailing to: poly-request@siam.org -
- or to: majordomo@wins.uva.nl -
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Today's Topics:
1. From opsftalk
2. 7th Krawtchouk Conference
3. SIAM Annual Meeting
4. Wilf and Zeilberger win Steele prize
5. Arno Kuijlaars receives 1998 Popov prize
6. Ian Macdonald to give plenary lecture at ICM
7. New journal "Fractional Calculus & Applied Analysis"
8. Maple qseries package
9. Special Issue on "Orthogonal Polynomials and Computer Algebra"
of the "Journal of Symbolic Computation"
10. Preprint Archive in Classical Analysis
11. Changes of Address, WWW Pages, etc.
12. Subscribing to OP-SF NET
13. Obtaining back issues of OP-SF NET and submitting contributions
to OP-SF NET and Newsletter
Calendar of Events:
1998
March 22-28: Meeting on Applications and Computation of Orthogonal
Polynomials, Oberwolfach, Germany 4.3 #6
May 14-16, 1998: 7th Krawtchouk Conference, Kiev, Ukraine 5.1 #2
May 16-22: Symmetries and Integrability of Difference Equations,
Sabaudia, Italy 4.5 #5
June 15-19: Formal Power Series and Algebraic Combinatorics,
Toronto, Canada 4.6 #3
June 21-25: q-Series, Combinatorics and Computer Algebra,
South Hadley, Massachusetts, USA 4.6 #4
June 29-July 2: Workshop on Orthogonal Polynomials: Numerical and Symbolic
Algorithms, Madrid, Spain 4.6 #5
July 8-10: Conference on Lattice Paths Combinatorics and Applications,
Vienna, Austria 4.6 #6
July 13-17: SIAM Annual Meeting, Toronto, Canada 5.1 #3
July 30 - August 7: International Workshop on Self-Similar Systems
Dubna, Russia 4.6 #7
Topic #1 ------------- OP-SF NET 5.1 ------------ January 15, 1998
From: OPSF Editor <muldoon@yorku.ca>
Subject: From opsftalk
As announced in OP-SF NET 4.6, Topic #27, opsftalk, a discussion forum in
orthogonal polynomials and special functions, is now open for business. To
subscribe, send a message to
majordomo@wins.uva.nl
and put in the body of the message only the words:
subscribe opsftalk
You can post messages by sending mail to
opsftalk@wins.uva.nl
Your message will then be automatically forwarded to everybody
on the opsftalk list.
Starting January 13, 1998, Tom Koornwinder is archiving postings to
opsftalk at the URL
http://turing.wins.uva.nl/~thk/opsftalk/archive.html
If the frequency of postings increases, then another (automatized)
solution for the archiving will be sought.
Many of the contributions to opsftalk will form the basis for Topics in
OP-SF NET. In addition, queries will, in most cases, be repeated in
this medium. We start, in this issue, with questions from Irving Segal and
Bozidar Anicin:
(1) Tom Koornwinder submitted Segal's question:
Dick Askey <askey@math.wisc.edu> communicated me on November 22, 1997 the
following question by Irving Segal <ies@math.mit.edu>. As Irving Segal
wrote, the question is relevant to theoretical physics and seems
mathematically interesting. As far as I know, the question has not yet
been answered by anybody.
Tom Koornwinder <thk@wins.uva.nl>
_____________________________________________
What is the kernel function for the Laguerre polynomials when the
variables are 2 by 2 hermitian matrices, rather than real?
The theorem of Sonine et al. (e.g., Szego's book page 101)
involves the product xy, which isn't symmetric in x and y and so can't be
right for the general case.
Has anyone worked on the case of matrix variables (I know of the
work of Ken Gross and others on Bessel functions of matrices, but it
doesn't clearly apply to the Laguerre context.)?
The question may come down to expressing a Bessel function of a
matrix (the 2 by 2 hermitian case is what I have) in a nice closed form in
terms of ordinary scalar Bessel functions, if that is possible. An
expression in terms of hypergeometric functions would be better than
nothing.
Irving Segal <ies@math.mit.edu>
(2) From Bozidar Anicin:
Problem A.
To prove, disprove or improve the following relation:
2 I_1(a) K_1(a) = \int_0^\infty g(z)cos(2az)dz / \int_0^\infty g(z) dz,
with g(z) = g(k) = (2/k -k) K(k) - (2/k) E(k) where K(k) and E(k) are
complete elliptic integrals of the first and second kind, respectively,
with the modulus k^2 = 1/(1+z^2). I_1 and K_1 are modified Bessel
functions of the first order. The variable z is real, "a" is also real,
but the possibility of complex "a" could also be considered.
Problem B
With the notation introduced in Problem A, to prove, disprove or improve
the following relation
\int_0^\infty g(z)dz = \pi/4.
That the two relations are at least approximately correct, stems
from electromagnetic theory. The left side in Problem A follows from
Maxwell's theory, the right side comes from the theory of RLC networks,
and the two sides represent the same physical quantity. Numerically, the
integral in problem B is (\pi/4)-0.002 with an approximate integrand.
Bozidar Anicin,
Faculty of Mechanical Engineering,
27 marta 80,
11000 Belgrade,
Yugoslavia
email: anicin@EUnet.yu
Topic #2 ------------ OP-SF NET 5.1 ------------ January 15, 1998
From: Vadim Zelenkov (zelenkov@isir.minsk.by)
Subject: 7th Krawtchouk Conference
I would like to inform you that 7th International Scientific Krawtchouk
Conference will be held on May 14-16, 1998 in National Technical
University of the Ukraine (Kiev).
It will include the following sections:
1. Differential and Integral Equations, their Application
2. Algebra, Geometry. Mathematical and Numerical Analysis
3. Probabilities Theory and Mathematical Statistics
4. History and Technique of Mathematical Teaching
See details on the Krawtchouk Polynomials Home Page
(http://www.isir.minsk.by/zelenkov/physmath/kr_polyn)
Vadim Zelenkov
Topic #3 ------------ OP-SF NET 5.1 ------------ January 15, 1998
From: OPSF Editor <muldoon@yorku.ca>
Subject: SIAM Annual Meeting
The 1998 Annual Meeting of the Society for Industrial and Applied
Mathematics will be held at the University of Toronto Canada, July
13-17, 1998. There is a partially overlapping SIAM Conference on Discrete
Mathematics July 12-15 and Society for Mathematical Biology (SMB) will be
running their annual meeting during the SIAM meeting. In addition the
Mathematical Association of America (MAA) MathFest will be held, also in
Toronto, on July 16-18.
The SIAM meeting will feature several invited talks including one by
George Andrews on "The Deconstruction of Calculus Reform" as well as
short courses and a rich variety of minisymposia.
Our Activity Group is exploring the possibility of a minisymposium on
"Problems and Solutions in Special Functions" but plans are not definite
at the time of going to press. Information will be maintained at our
website (http://www.math.yorku.ca/siamopsf/) and distributed via opsftalk.
Another minisymposium of possible interest to our readers is
"Symbolic-Numeric Algorithms for Polynomials" organized by Robert Corless
and Stephen H. Watt.
Information on the SIAM meeting is available at the URL:
http://www.siam.org/meetings/an98/an98home.htm
Topic #4 ------------ OP-SF NET 5.1 ------------ January 15, 1998
From: Tom H. Koornwinder <thk@wins.uva.nl>
Subject: Wilf and Zeilberger win Steele prize
On January 13, 1998 I received a message from Doron Zeilberger to his
E-friends that Herbert Wilf and Doron Zeilberger were awarded the 1998
Steele prize. He added the responses of Herbert Wilf and himself to this
prize, see below. I congratulate Herbert and Doron on this well-deserved
award.
Tom Koornwinder
------------------------------------------------
Response to the Award of the 1998 Steele Prize
by Doron Zeilberger <zeilberg@euclid.math.temple.edu>
[Generic Thanks and Expressions of Astonishment.]
On 11:05 PM, Dec. 24 (sic!) 1988, Herb Wilf called me up, and with Wilfian
enthusiasm, told me how the beautiful one-line proofs of certain classical
identities, generated by my beloved computer, Shalosh B. Ekhad, could be
made even prettier, and how to obtain as a bonus, a `dual identity', that
is often much more interesting than the one originally proved. Thus was
born WZ theory.
WZ theory has taught me that computers, by themselves, are not yet capable
of creating the most beautiful math. Conversely, humans do much better
math in collaboration with computers. More generally, combining different
and sometimes opposite approaches and viewpoints will lead to revolutions.
So the moral is: Don't look down on any activity as inferior, because two
ugly parents can have beautiful children, and a narrow-minded or elitist
attitude will lead nowhere.
We live in the great age of the democratization of knowledge, and even of
that elitist ivory-tower called mathematics. Whoever would have believed,
thirty years ago, that a 1988 Steele prize would go to Rota for his work
in `combinatorics' (a former slum), and whoever would have believed ten
years ago that a 1998 Steele prize would go to W and Z for their work on
`binomial coefficients identities' (hitherto a slum squared).
The computer-revolution, and especially the World Wide Web, is quickly
making mathematics accessible and enjoyable to many more people.
Especially commendable are the wonderful website of Eric Weisstein's `Eric
Treasure Troves', Steve Finch's pages on mathematical constants, the
Sloane-Plouffe On-Line Encyclopedia of Integer Sequences, Simon Plouffe's
`Inverse Symbolic Calculator', and St. Andrews University's MacTutor site
on the history of mathematics.
It is very important to make information, in particular mathematical,
freely accessible. The pioneering, and extremely successful, Electronic J.
of Combinatorics, created by Herb Wilf in 1994, should be emulated. It is
very regrettable that the American Mathematical Society has
subscription-only electronic journals, and that the electronic versions of
its paper journals are only available to paper-subscribers. It is a
disgrace that MathSciNet is only viewable for paying customers, thereby
making its contents unsearchable by public search-engines.
On the positive side, the AMS has been very efficient in taking advantage
of the electronic revolution, and the free ERA-AMS, under the leadership
of Svetlana Katok, is a real gem!
I am really happy, not only for myself and Herb, but also because of the
recognition that the field of hypergeometric series (alias binomial-
coefficients identities) is hereby granted. There are so many giants on
whose shoulders we are standing. Guru Dick Askey, q-Guru George Andrews,
and Guru Don Knuth who preached the gospel from the continuous and
discrete sides. Sister Celine Fasenmyer, a non-standard, yet very tall,
giant. Hacker Bill Gosper who deserves this prize even more, and many
others.
I should also mention our collaborators in this area: Gert Almkvist and
Marko Petkovsek, and the beautiful work of Tewodros Amdeberhan, Frederic
Chyzak, J. Hornegger, Bruno Gauthier, Ira Gessel, Wolfram Koepf, Christian
Krattenthaler, John Majewicz, Istvan Nemes, John Noonan, Sheldon Parnes,
Peter Paule, Bruno Salvy, Marcus Schorn, Volker Strehl, Nobuki Takayama,
P. Verbaeten, Kurt Wegschaider, and Lily Yen.
Finally, I must mention my main influencers, in roughly chronological
order. My terrific seventh-grade math teacher, Devorah Segev, and my
great eighth-grade history teacher (and principal), Matityahu Pines. My
cousin Mati Weiss, who showed me Joe Gillis's `Gilyonot leMatematika'. Joe
Gillis, who in my early teens, first made me into a mathematician through
his `Gilyonot leMatematika'. My advisor, Harry Dym, who initiated me into
research. My god-advisor, Dick Duffin, who discretized me. Leon
Ehrenpreis, who dualized me. Joe Gillis (again!) who deranged me.
Gian-Carlo Rota who umbralized me. Dick Askey, who hypergeometrized me.
George Andrews who q-ified me. Herb Wilf (the same Herb!) who
combinatorized me. Dominique Foata, who bijectified me. Jet Wimp, who
asymptotized me. Xavier Viennot, who Schutzenbergerized me. Marco
Schutzenberger, who formalized me. Bruno Buchberger, who basically
standardized [grobnerized] me. Gert Almkvist who integralized me, and
Pierre Cartier, who Bourbakised me. Let them all be blessed!
-------------------------------------------------
Response of Herbert Wilf <wilf@math.upenn.edu> :
I am deeply honored to receive the Leroy P. Steele Prize. I might say that
doing this research was its own reward -- but it's very nice to have this
one too! My thanks to the Selection Committee and to the AMS.
Each semester, after my final grades have been turned in and all is quiet,
it is my habit to leave the light off in my office, leave the door closed,
and sit by the window catching up on reading the stack of preprints and
reprints that have arrived during the semester. That year, one of the
preprints was by Zeilberger, and it was a 21st century proof of one of the
major hypergeometric identities, found by computer, or more precisely,
found by Zeilberger using his computer. I looked at it for a while and it
slowly dawned on me that his recurrence relation would assume a self dual
form if we renormalize the summation by dividing first by the right hand
side. After that normalization, the basic "WZ" equation
F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k) appeared in the room, and its self-dual
symmetrical form was very compelling. I remember feeling that I was about
to connect to a parallel universe that had always existed but which had
until then remained well hidden, and I was about to find out what sorts of
creatures lived there. I also learned that such results emerge only after
the efforts of many people have been exerted, in this case, of Sister Mary
Celine Fasenmyer, Bill Gosper, Doron Zeilberger and others. Doing joint
work with Doron is like working with a huge fountain of hormones - you
might get stimulated to do your best or you might drown. In this case I
seem to have lucked out. It was a great adventure.
Topic #5 ------------ OP-SF NET 5.1 ------------ January 15, 1998
From: Tom Koornwinder <thk@wins.uva.nl>
Subject: Arno Kuijlaars receives 1998 Popov prize
The following is based on a message from Prof. Jaap Korevaar
<korevaar@wins.uva.nl> and on the URL
http://math.vanderbilt.edu/events/approx.html
I congratulate Arno.
Tom Koornwinder <thk@wins.uva.nl>
---------------------------------------------------------
On January 4, 1998 Dr. A.B.J. ("Arno") Kuijlaars received the
international Popov prize.
The second Vasil A. Popov Prize was awarded at the Ninth Texas
International Conference on Approximation Theory held in January 1998 in
Nashville, Tennessee. The prize has been established in memory of Vasil
A. Popov and his contributions to approximation theory and related areas
of mathematics.
The prize is awarded every three years for outstanding research
contributions in fields related to Vasil Popov's work. Albert Cohen was
the first recipient of the Vasil A. Popov Prize awarded in 1995.
Eligibility for the current prize was restricted to mathematicians who did
not have their terminal degree on June 1, 1991. The winner of the prize
was asked to deliver a plenary lecture at the Texas conference.
The Selection Committee for the Vasil A. Popov Prize consisted of Charles
Chui, Ronald A. DeVore, Paul Nevai, Alan Pinkus, Pencho Petrushev, and
Edward Saff.
Arno received the prize for his innovating applications of potential
theory to various problems from approximation theory. Nowadays this
concerns in particular the accurate study of equilibrium distributions on
a conductor in the presence of an exterior field; cf. [1].
Kuijlaars obtained his PhD in 1991 at the University of Utrecht on a topic
from abstract potential theory, under the guidance of Prof. E.M.J. Bertin.
He started with his present, more concrete work as a post-doc at the
University of Amsterdam (1992-1995) under the guidance of Prof. J.
Korevaar. He also worked for a short period with the well-known
approximation theory specialist Prof. E. Saff at the University of South
Florida (Tampa), with the numerical analyst Prof. W. Gautschi at Purdue
University (Lafayette, Indiana) and with the approximation theory
specialist Prof. W. Van Assche in Leuven (Belgium). At the moment he is
working at the City University of Hong Kong with Prof. R. Wong. He will
soon take up a more permanent position at the Katholieke Universiteit
Leuven.
Kuijlaars' current e-mail address is: maarno@math.cityu.edu.hk
_________
[1] E.B. Saff and V. Totik, Logarithmic potentials with external fields.
Grundlehren der Math. Wissenschaften, vol. 316, Springer, Berlin, 1997.
Topic #6 ------------ OP-SF NET 5.1 ------------ January 15, 1998
From: Tom H. Koornwinder <thk@wins.uva.nl>
Subject: Ian Macdonald to give plenary lecture at ICM
Ian G. Macdonald (Queen Mary and Westfield College, University of London,
England) is one of 21 mathematicians invited to give one-hour Plenary
Lectures at ICM-98, the International Congress of Mathematicians, to be
held in Berlin, Germany, August 18-27, 1998. This invitation was issued
by the Organizing Committee on the recommendation of the Program Committee
appointed by the International Mathematical Union (IMU).
This information is taken from the IMU website at the URL
http://elib.zib.de/ICM98/B/2
Topic #7 ------------ OP-SF NET 5.1 ------------ January 15, 1998
From: Virginia Kiryakova <virginia@math.acad.bg>
Subject: New journal "Fractional Calculus & Applied Analysis"
The Editorial Board of
"Fractional Calculus & Applied Analysis" (FCAA)
(An International Journal for Theory and Applications)
are pleased to announce the launching of this new journal
(vol 1, 1998), specialized on the subjects:
Fractional Calculus, Integral Tranforms, Special Functions and other
closely related topics of Applied Analysis.
Addresses for contacts:
"FCAA" Journal
Dr. Virginia Kiryakova (Managing Editor)
Institute of Mathematics & Informatics
Bulgarian Academy of Sciences, Sofia 1090
Bulgaria
email: fcaa@math.acad.bg
URL: http://alef.math.acad.bg/~fcaa
(comment by editor OPSF-NET: the URL could not yet be reached when I
tried)
Topic #8 ------------ OP-SF NET 5.1 ------------ January 15, 1998
From: Wolfram Koepf <koepf@imn.htwk-leipzig.de>
Subject: Special Issue on "Orthogonal Polynomials and Computer Algebra"
of the "Journal of Symbolic Computation"
I would like to remind you that Dick Askey, Tom Koornwinder and I
are co-editing a special issue of the "Journal of Symbolic Computation"
on "Orthogonal Polynomials and Computer Algebra", see
http://www.zib.de/koepf/jsc
or
http://www.cis.udel.edu/~caviness/jsc.html
http://www.cis.udel.edu/~caviness/jsc/specialIssues/orthogonalPolys.html
The deadline for submissions was Jan. 15, 1998. I would like to inform
you that this deadline will be extended by a short period, and encourage
everybody to finish their papers, and send them within the next four
weeks.
If you want to publish a paper in this issue, please send me a message
(preferably to my old e-mail address koepf@zib.de) to announce this fact
and indicate when your paper will be finished.
Submissions should be also sent to me.
Topic #9 ------------ OP-SF NET 5.1 ------------ January 15, 1998
From: Frank Garvan <frank@math.ufl.edu>
Subject: Maple qseries package
FOLKS:
I have written a Maple package called "qseries".
Documentation, installation instructions, files etc
are available via WWW:
http://www.math.ufl.edu/~frank/qmaple/qmaple.html
The package contains a bunch of Maple programs for computing with
q-series. At present, the main features are
* Conversion of q-series to infinite products of different types
including eta-products and theta products.
* Generating probable algebraic relations (if they exist) among
given q-series.
At present there is one version:
* UNIX
In the near future I hope to create a version for
* WINDOWS 3.1x
(Hey - my pc at home runs win3.1)
I have tested the programs on both Maple V Release 3 and Release 4 and
they seem to work ok. Please report any bugs, typos, suggestions,
compliments and complaints. Should I change the name of the package?
Maybe I should call it _qprods_ instead of _qseries_.
Cheers,
Frank Garvan
(frank@math.ufl.edu)
Topic #10 ------------ OP-SF NET 5.1 ------------ January 15, 1998
From: Tom Koornwinder <thk@wins.uva.nl>
Subject: Preprint Archive in Classical Analysis
I call your attention to a recent restructuring of electronic
archives for preprints in Mathematics, like the existing q-alg.
Read more about this in
http://xxx.lanl.gov/new/math.html
One of the proposed new archives is:
CA - Classical Analysis
Harmonic analysis, approximations, series, expansions, asymptotics,
classical transforms, special functions, differential relations,
exact ODE's, calculus of variations
Topic #11 ------------ OP-SF NET 5.1 ------------ January 15, 1998
From: OP-SF NET Editors <thk@wins.uva.nl>, <muldoon@yorku.ca>
Subject: Changes of Address, WWW Pages, etc.
Renato Alvarez-Nodarse writes:
Effective December 1, 1997 my e-mail address will be nodar@math.uc3m.es
The former address renato@dulcinea.uc3m.es will still be valid, although
only for a short period. Please update aliases/records to the new one.
Dharma P. Gupta is now the President of the Allahabad Mathematical
Society, publishers of the Indian Journal of Mathematics. His current
address is:
19B Hastings Road,
Ashoknagar,
ALLAHABAD 211001, India
Semyon Yakubovich has moved recently to a post-doctoral position in
Eindhoven. His address there is:
Dept. of Mathematics and Computing Sciences
Eindhoven University of Technology
P.O.Box 513
5600 MB Eindhoven
The Netherlands
e-mail: semyon@win.tue.nl
Topic #12 ------------ OP-SF NET 5.1 ------------ January 15, 1998
From: OP-SF NET Editors <thk@wins.uva.nl>, <muldoon@yorku.ca>
Subject: Subscribing to OP-SF NET
There are two ways to subscribe to OP-SF NET:
1. Send a message to
poly-request@siam.org
with your name and email address in the body of the message. If
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OP-SF NET which is maintained by SIAM.
2. Send a message to
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and put in the body of the message only the words:
subscribe opsfnet
This is handled by an automatic list server. You will receive a
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people on the list maintained by SIAM.
Topic #13 ------------ OP-SF NET 5.1 ------------ January 15, 1998
From: OP-SF NET Editors <thk@wins.uva.nl>, <muldoon@yorku.ca>
Subject: Obtaining back issues of OP-SF NET and submitting contributions
to OP-SF NET and Newsletter
Back issues of OP-SF NET can be obtained from
ftp: ftp.wins.uva.nl, in directory
pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir
or WWW: http://turing.wins.uva.nl/~thk/opsfnet/
or WWW: http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html
Contributions to the OP-SF NET 5.2 should reach the email address
poly@siam.org before March 1, 1998.
The Activity Group also sponsors a (printed) Newsletter edited by Wolfram
Koepf. Deadline for submissions to be included in the February 1998 issue
is January 15, 1998 and for the June 1998 issue it is May 15, 1998.
Please send your Newsletter contributions directly to the Editor:
Wolfram Koepf
Fachbereich IMN
HTWK Leipzig
Gustav-Freytag-Str. 42 A
D-04277 Leipzig
phone: +49-341-307 64 95
fax: +49-341-301 27 22
e-mail: koepf@imn.htwk-leipzig.de
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
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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
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