o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - - - 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 - - - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o 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 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 communicated me on November 22, 1997 the following question by Irving Segal . 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 _____________________________________________ 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 (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 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 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 [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 : 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 Subject: Arno Kuijlaars receives 1998 Popov prize The following is based on a message from Prof. Jaap Korevaar and on the URL http://math.vanderbilt.edu/events/approx.html I congratulate Arno. Tom Koornwinder --------------------------------------------------------- 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 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 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 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 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 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 , 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 , 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 everything works well, you will be put on the mailing list of OP-SF NET which is maintained by SIAM. 2. Send a message to majordomo@wins.uva.nl 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 confirmation, with a list of further commands. You will be put on the opsfnet mailing list of this list server. A new issue of OP-SF NET will be mailed to people on this list immediately after the mailing by SIAM to the people on the list maintained by SIAM. Topic #13 ------------ OP-SF NET 5.1 ------------ January 15, 1998 ~~~~~~~~~~~~~ From: OP-SF NET Editors , 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 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. Student memberships are $20 a year with free membership in one Activity Group. Postgraduates can join for $45 a year (for three years). Contact the email address join@siam.org 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. 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Temme, Secretary - - Willard Miller, Jr., Program Director - - The appointed officers are: - - Wolfram Koepf, Newsletter editor - - Martin Muldoon, Webmaster and OP-SF NET editor - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o