o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - - - December 29, 1994 - - O P - S F N E T Volume 1, Number 9 - - ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - - Tom H. Koornwinder, Editor thk@fwi.uva.nl - - - - - - 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 - - - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o Today's Topics: 1. Orthogonal polynomials and special functions in BAMS, January, 1995 2. In Memoriam P.J. de Doelder 3. Pictures wanted 4. First Maghrebian Colloquium on Analysis 5. New Maple package: summation 6. Urgent research question 7. Call for conjectures to be tested by undergraduate students 8. New errata for the book Basic hypergeometric series 9. Changes of address 10. WWW server for Journal of Approximation Theory 11. hep-th and q-alg archives 12. Recent additions to ftp site on orthogonal polynomials and related special functions 13. Obtaining back issues and contributing to future issues of OP-SF Net and the Newsletter Calendar of events: see issue/topic: 1995 January 8-12: Conference on Approximation Theory, College Station, 1.4 #7 January 16-27: Conference on Exponential Asymptotics, Cambridge, UK 1.8 #11 March 17-18: Session "Approximation Theory and Special Functions" 1.7 #6 March 20-22: Stieltjes Colloquium in Toulouse 1.7 #7 May 29-June 2: Formal Power Series and Combinatorics, Paris 1.8 #13 June 9-10: Lee Lorch Conference 1995 1.7 #8 June 12-23: Fields Institute program on Special functions etc. 1.7 #9 July 3-7: Minisymposium at ICIAM '95, Hamburg: "Orthogonal Polynomials and Spectral Methods" 1.8 #16 July 19-21: First Maghrebian Colloquium on Analysis 1.9 #4 Topic #1 -------------- OP-SF NET --------------- December 29, 1994 ~~~~~~~~~ From: Dick Askey Subject: Orthogonal polynomials and special functions in BAMS, January, 1995 Orthogonal polynomials and special functions in Bull. Amer. Math. Soc., January, 1995. The survey paper in this issue is "How many zeros of a random polynomial are real?" by Alan Edelman and Eric Kostlan. In the paper a tridiagonal matrix is given, what is now called the Kac matrix. This is an (n+1)x(n+1) matrix with zeros on the main diagonal, the integers 1,2,...,n below the main diagonal and this sequence backwards above the main diagonal, with the sequences starting in the upper left. The eigenvalues are -n,-n+2,-n+4,...,n-2,n. A reference for this and the history is given to a paper by John Todd and Olga Tausky in Linear Algebra Appl. 150 (1991), 341-360. In fact, this matrix appeared much earlier than in Mark Kac's nice paper "Random walk and the theory of Brownian motion", Amer. Math. Monthly 54 (1947), 369-391. It comes from the symmetric Krawtchouk polynomials, and the fact that the eigenvalues are the integers above is just a reflection of the location of the point masses for the Krawtchouk polynomial orthogonality. This is usually given as the integers 0,1,...,n, but when the distribution is symmetric there is a case for having the symmetry about x=0, which is what was done here. There are many other such matrices. The most general one coming from classical type orthogonal polynomials comes from the q-Racah polynomials, and was treated by Askey and Wilson in SIAM J. Math. Anal. 10 (1979), 1008-1016. Kac's Monthly paper can be completely rewritten using orthogonality of symmetric Krawtchouk polynomials to obtain his main results. Mark Kac loved orthogonal polynomials, and once told me that he learned the theorem we attribute to Favard in a book by Wintner, published in 1929. However, I don't think he knew about Krawtchouk polynomials when he died and so was not aware that his Monthly paper could be redone in an easier way. The book review of Deligne and Mostow's book "Commensurabilities among lattices in PU(1,n)" written by Cohen and Hirzebruch is worth reading whether you read the book or not. It may even be more important for most of us to read if we are going to read the book, for the essential connection with hypergeometric functions in one and several variables is spelled out very nicely in the review. I would appreciate other references to uses of special functions in the published literature. This could be a use of our newsletter. Topic #2 -------------- OP-SF NET --------------- December 29, 1994 ~~~~~~~~~ From: J. Boersma Subject: In Memoriam P.J. de Doelder In OP-SF Net 1.8, topic #7 it was already briefly mentioned that P.J. de Doelder died on October 16, 1994. J. Boersma sent us the following. In memoriam P.J. de Doelder Pieter J. de Doelder, retired from Eindhoven University of Technology, died on October 16, 1994 at the age of 75 years. From 1957 till 1982 de Doelder was a faculty member of the Department of Mathematics of EUT, where he was primarily involved in teaching. In addition, de Doelder was a prolific problem solver, particularly in the field of special functions. Till the end of his life he made numerous contributions to the Problem Sections of Nieuw Archief voor Wiskunde, SIAM Review, and of the OP-SF Newsletter. Topic #3 -------------- OP-SF NET --------------- December 29, 1994 ~~~~~~~~~ From: Eugene Tomer Subject: Pictures wanted If you happen to be at a meeting somewhere, or even if you don't, you might carry along your photographic apparatus and take a few pictures. The Newsletter of our Activity Group will print them so your friends can see you have actually been there, or somewhere. See the last section of the Newsletter on how to contribute photographic material. Topic #4 -------------- OP-SF NET --------------- December 29, 1994 ~~~~~~~~~ From: A. Bakali Subject: First Maghrebian Colloquium on Analysis The first "Maghrebian Colloquium on Analysis" will be held in Kenitra, Morocco during July 19-21, 1995. It is the intention that such a colloquium will be organized yearly in one of the countries of the Maghreb region. The next one will be held in Tunisia. It is open to mathematicians from all countries. The fields of interest of this first meeting are: I) Harmonic Analysis II) Functional Analysis and Applications III) Potential Theory and Probability Theory More particular attention will be paid to the following topics: Representation theory, Spherical and special functions, Gelfand pairs and their generalizations, Hypergroups, Operator theory and applied functional analysis, Potential theory and Probability theory. The working languages will be English and French. The meeting will include plenary lectures and short communications in the three parallel sessions I), II) and III). If you are interested in participating, please contact prof. Bakali as soon as possible at the address below, and mention if you want to give a lecture (plenary or short communication). A. Bakali Equipe d'Analyse Departement de Mathematiques et d'Informatique Faculte des Sciences Universite Ibn Tofail BP 133, Kenitra Morocco fax: +212-7-37 27 70 Topic #5 -------------- OP-SF NET --------------- December 29, 1994 ~~~~~~~~~ From: Wolfram Koepf Subject: New Maple package: summation Maple package: summation Authors: Wolfram Koepf and Gregor St\"olting email: koepf@zib-berlin.de Date: December 1994 This package is an implementation of the Gosper and Zeilberger algorithms for indefinite and definite summation covering extensions given by Koepf. The program is done on the lines of Tom Koornwinder's program zeilb. References: [1] R. W. Gosper, Jr.: Decision procedure for indefinite hypergeometric summation, Proc. Nat. Acad. Sci. USA 75 (1978), 40-42. [2] T. H. Koornwinder: On Zeilberger's algorithm and its q-analogue: a rigorous description. J. of Comput. and Appl. Math. 48 (1993), 91-111. [3] D. Zeilberger, A fast algorithm for proving terminating hypergeometric identities, Discrete Math. 80 (1990), 207-211. The extensions are described in [4] W. Koepf: Algorithms for the indefinite and definite summation. Konrad-Zuse-Zentrum Berlin (ZIB), Preprint SC 94-33 (Dezember 1994). (see /ftp/pub/koepf/summation.tex or summation.ps in W. Al-Salam's archive, ftp euler.math.ualberta.ca) The package comes with a test file summation.tst including many examples. Topic #6 -------------- OP-SF NET --------------- December 29, 1994 ~~~~~~~~~ From: Ernst Davidovich Krupnikov Subject: Urgent research question Dear colleagues: who knows if anything has been done on generalizations of summation theorems of Bailey and Whipple, Gauss (second) and Watson, Kummer and Dixon? Please email me corresponding references on this topic. Ernst Davidovich Krupnikov email: ernst@net.neic.nsk.su Topic #7 -------------- OP-SF NET --------------- December 29, 1994 ~~~~~~~~~ From: Alan Schwartz Subject: Call for conjectures to be tested by undergraduate students William C. Connett and Alan L. Schwartz are using NSF funding to organize a computational laboratory for undergraduate students. A typical activity to test mathematical conjectures about orthogonal polynomials and other special functions. We would like to share this resource widely and we seek problems for these students to work on. Currently students are using Maple to look at positivity of linearization coefficents and to answer questions about the maximum of certain specific families of polynomials. If you would like to submit conjectures or if you have questions please contact Alan L. Schwartz or William C. Connett schwartz@arch.umsl.edu connett@umslvma.bitnet (314) 553-6719 (314) 553-6343 Department of Mathematics and Computer Science University of Missouri - St. Louis St. Louis, MO 63121 There will be a few summer research assistantships for undergraduates to participate in this program. Interested students should send inquiries to the address above (snailmail or email) Topic #8 -------------- OP-SF NET --------------- December 29, 1994 ~~~~~~~~~ From: George Gasper Subject: New errata for the book Basic hypergeometric series Errata, updates of the References, etc., (as of Dec. 27, 1994) for the book Basic Hypergeometric Series, by George Gasper and Mizan Rahman, Encyclopedia of Mathematics and its Applications, Vol. 35, Cambridge University Press, Cambridge-New York, 1990 are now available on file from George Gasper (and probably soon also as file /ftp/pub/gasper-rahman.tex in W. Al-Salam's archive, ftp euler.math.ualberta.ca). Below are the errata added to the list since November 19, 1993: p. 212, eq. (8.7.13): Insert the factor `` $(q; q)_s$ '' into the denominator on the right side of the equation. p. 191, Ex. 7.32 (ii): Insert the factor `` $q^{(\alpha - \beta) n/2}$ '' after the `` $(-1)^n$ '' factor on the right side of the equation. p. 275: In Wilson [1978] change ``polynomials'' to ``functions'' . p. 167, eq. (7.3.13): Replace the factor $(-ac)^n$ by $(-acq^2)^{-n}$ . Topic #9 -------------- OP-SF NET --------------- December 29, 1994 ~~~~~~~~~ From: OP-SF Net Editor Subject: Changes of address Eric Opdam (University of Leiden) will stay during January-June 1995 at: University of Michigan, Math. Dept. Ann Arbor, MI 48109-1003 USA Marcel de Jeu, who recently got his Ph.D at the University of Leiden and who is, like Eric Opdam, a specialist in the area of special functions associated with root systems, will stay during 15 January - 15 July 1995 as a postdoc at: MIT, Dept. of Math. Cambridge, MA 02139 USA Topic #10 ------------- OP-SF NET --------------- December 29, 1994 ~~~~~~~~~ From: Paul Nevai Subject: WWW server for Journal of Approximation Theory It is our pleasure to announce the establishment of a WWW server for Journal of Approximation Theory at: http://math.ohio-state.edu/Groups/JAT This home page for JAT, still in development, contains large, easily usable address and e-mail lists of people in Approximation Theory, as well as tables of contents and additional information for authors and readers of JAT. Sincerely, Paul Nevai and Allan Pinkus Editors-in-Chiefs J. Approx. Theory Topic #11 ------------- OP-SF NET --------------- December 29, 1994 ~~~~~~~~~ From: Net Editor Subject: hep-th and q-alg archives The hep-th electronic archive contains preprints in the area of theoretical high energy physics (string, conformal and field theory). A lot of material involving special functions and orthogonal polynomials can be found there, in particular quantum groups related q-stuff. Since last week, new q-algebra preprints are being redirected to a new archive q-alg (quantum algebra including knot theory). The email and WWW addresses of the two sites are as follows: hep-th: email: hep-th@xxx.lanl.gov or hep-th@babbage.sissa.it WWW: http://xxx.lanl.gov/hep-th q-alg: email: q-alg@eprints.math.duke.edu WWW: http://www.msri.org/preprints Send an email message to one of the two sites and put the word "help" on the subject line if you want to receive more information. Topic #12 ------------- OP-SF NET --------------- December 29, 1994 ~~~~~~~~~ From: Waleed A. Al-Salam Subject: Recent additions to ftp site on orthogonal polynomials and related special functions Waleed Al-Salam has an anonymous ftp site at euler.math.ualberta.ca on orthogonal polynomials and related special functions. It can also be accessed by using World Wide Web (xmosaic or Mosaic) at the address ftp://euler.math.ualberta.ca. Manuscripts can be obtained from directory pub and subdirectories. In particular, examine the CONTENTS file in the pub directory. If you wish to receive periodic info regarding recent additions to this database please send an email message to waleed@euler.math.ualberta.ca with your e-mail address. You are invited to submit one or more of your not-yet-in-print manuscripts which you wish to make available to the general OPS community. They should be in Plain TeX, LaTeX, AMSTeX or AMSLaTeX format. These manuscripts can be submitted by one of the following methods: a) E-mail to waleed@EULER.MATH.UALBERTA.CA b) anonymous ftp to euler.math.ualberta.ca then "cd submissions" and finally "put file" where "file" is the name of the file you wish to deposit. Between November 11 and December 27, 1994 the following additions were put in the pub directory: M. L. Glasser, The quadratic formula made hard, a less radical approach to solving equations. (see /ftp/pub/glasser.tex) V. B. Kuznetsov, 3F2(1) hypergeometric function and quadratic R-matrix algebra. (see /ftp/pub/kuznetsov_QISM2_hahn.tex) T. H. Koornwinder, Special functions associated with rootsystems: recent progress. (see /ftp/pub/koornwinder4.ps) D. P. Gupta and D. Masson, Contiguous relations, continued fractions and orthogonality: an 8phi7 model. (see /ftp/pub/massonc.tex) V. Kowalenko and M.L. Glasser, Extensions and results from a method for evaluating fractional integrals. (see /ftp/pub/glasser/glasser4.tex+ revtex sty files) P. G. A. Floris, Addition formula for q-disk polynomials. (see /ftp/pub/floris1.tex) P. G. A. Floris, A noncommutative discrete hypergroup associated with q-disk polynomials. (see /ftp/pub/floris2.tex) R. Askey, M. Rahman and S. Suslov, On a general q-Fourier transformation with non-symmetric kernel. (see /ftp/pub/askey-rahman-suslov.tex). P. I. Etingof and A. A. Kirillov, Representation-theoretic proof of the inner product and symmetry identities for Macdonald's polynomials. (see /ftp/pub/ident.ps ). H. T. Koelink, Addition formula for 2-parameter family of Askey-Wilson polynomials (see /ftp/pub/koelink4.tex). W. Koepf, Algorithms for the indefinite and definite summation. (see /ftp/pub/koepf/summation.tex or summation.ps) W. Koepf, Reduce package for the indefinite and definite summation. (see /ftp/pub/koepf/sumreduce.tex or sumreduce.ps) W. Koepf, Algebraische Darstellung tranzendenter Funktionen. (see /ftp/pub/koepf/tranz.tex or tranz.ps) H. T. Koelink and J. Verding, Spectral analysis and the Haar functional on the quantum SU(2) group. (see /ftp/pub/koelink-verding.tex) Topic #13 -------------- OP-SF NET --------------- December 29, 1994 ~~~~~~~~~ From: Tom H. Koornwinder Subject: Obtaining back issues and contributing to future issues of OP-SF Net and the Newsletter Back issues of OP-SF Net can be obtained from ftp: ae.siam.org, in directory pub/opsf-net . or gopher: gopher.siam.org or WWW: gopher://gopher.siam.org Contributions to the OP-SF Net 2.1 should reach the email address poly@siam.org before February 1, 1995. Contributions to the Spring issue of the Orthogonal Polynomials and Special Functions Newsletter should reach the Editor Eugene Tomer before February 10, 1995. Items for the Newsletter without mathematical symbols can be submitted in any convenient form, for example as a textfile or as a typewritten manuscript. Items containing substantial mathematical symbols must be submitted as a standard Latex file by e-mail or by disc. There is only one exception: plain TeX files can be accepted by making special arrangements with the Editor. AmsTeX and AmsLatex files cannot be accepted. Whatever the content of your Latex article, you must use a certain preamble which can be obtained by e-mail from the Editor. Eugene Tomer Applied Mathematics & Computing 150 Hernandez Avenue San Francisco, CA 94127, USA fax +1-415-731 3551 Contributions to either the Net or to the Newsletter will be automatically considered also for inclusion in the other medium. o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - 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. - - Submissions with sufficiently long useful life will also be - - considered automatically for our quarterly printed newsletter. - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - Send submissions to: poly@siam.org - - Send address changes to: poly-request@siam.org - - Get back issues by ftp from: ae.siam.org (directory pub/opsf-net) - - or gopher: gopher.siam.org - - or WWW: gopher://gopher.siam.org - - Information on joining SIAM - - and this activity group: service@siam.org - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - The Officers of the Activity Group are: - - - - Charles Dunkl, Chair - - George Gasper, Vice Chair - - Tom H. Koornwinder, Secretary and OP-SF Net Editor - - Martin E. Muldoon, Program Director - - Eugene Tomer, Newsletter Editor - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o