o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - - - 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 - - - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o 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. 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 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 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 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 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 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 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 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 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 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 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 . 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 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 , 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 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 . 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. - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - Send submissions to: poly@siam.org - - Send address changes to: poly-request@siam.org - - Get back issues by ftp from: ftp.fwi.uva.nl, in directory - - pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir - - WWW home page of this Activity Group: - - http://www.math.yorku.ca/Who/Faculty/Muldoon/siamopsf/ - - Information on joining SIAM - - and this activity group: service@siam.org - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - The elected Officers of the Activity Group are: - - Charles Dunkl, Chair - - Tom H. Koornwinder, Vice Chair and OP-SF Net editor - - Nico M. 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