O P - S F N E T Volume 8, Number 2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Editor: 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: listproc@nist.gov o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o Today's Topics: 1. Planned activities (Activity Group Chair) 2. Request for Information for DLMF Project 3. opsftalk 4. Delft Workshop on Quantum Groups and Special Functions 5. Workshop on Advanced Special Functions in Italy 6. Benin Workshop on Mathematical Physics 7. IMA Program on "Special Functions in the Digital Age" 8. Report on AMADE-2001 9. Book by Dunkl and Xu on Orthogonal Polynomials of Several Variables 10. Book on Orthogonal Polynomial for Exponential Weights 11. Book by Schoutens on Stochastic Processes and Orthogonal Polynomials 12. Further information on the Hong Kong Proceedings 13. Maple packages for hypergeometric summation 14. OP-SF preprints in xxx archive 15. Changes of Address, WWW pages, etc. 16. About the Activity Group 17. Submitting contributions to OP-SF NET and Newsletter Calendar of Events: 2001 April 9: Workshop on Quantum Groups and Special Functions, Delft, The Netherlands 8.2 #4 April 17-20: Conference "Applications of the Macdonald Polynomials", Newton Institute, Cambridge, UK 7.5 #2, 8.1 #2 June 18-22: Symposium on Orthogonal Polynomials, Special Functions and Applications, Rome, Italy 7.3 #2, 8.1 #3 June 24-29: Workshop on "Advanced Special Functions and Related Topics in Probability and in Differential Equations", Melfi, Italy 8.2 #5 June 25 - July 6: Workshop "The Macdonald Polynomials", Newton Institute, Cambridge, UK 7.5 #2 July 2-12: Summer School on Applied Analysis, Hong Kong 7.5 #3 July 9-13: SIAM Annual Meeting, San Diego, California, USA See: http://www.siam.org/meetings/an01/ July 9-22: Summer School in Asymptotic Combinatorics, St. Petersburg, Russia 7.6 #3 August 6-10: Analytic theory of continued fractions, orthogonal functions and related topics, Grand Junction, Colorado, USA 7.4 #5 August 20-24: 3rd International meeting on Approximation Theory, Dortmund, Germany 7.4 #6 October 1-5: "Numerical Algorithms", Conference in Honor of Claude Brezinski, Marrakesh, Morocco 7.3 #3 October 28 - November 2: Workshop on Mathematical Physics, Porto-Novo, Benin 8.2 #6 2002 July 22 - August 2: IMA Summer Program "Special Functions in the Digital Age" Minneapolis, Minnesota, USA 8.2 #7 August 5-14: Workshop on Special Functions at FoCM'02, "Foundations of Computational Mathematics" Minneapolis, Minnesota, USA 8.1 #1 Future plans: * There are plans to organize summer schools on "Orthogonal Polynomials and Special Functions" in Europe during the coming three years: - 2001 (probably September): in Germany (contact person: Rupert Lasser ) - 2002 : in the Netherlands or Belgium (contact person: Erik Koelink - 2003 (time undecided): in Portugal (contact person: Amilcar Branquinho). The coordinator of the three summer schools is Erik Koelink (koelink@dutiaw4.twi.tudelft.nl). These summer schools are part of our Activity Group's scientific program. The scientific committee consists of Erik Koelink, Rupert Lasser, Amilcar Branquinho, Paco Marcellan and Walter Van Assche. Topic #1 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: Daniel Lozier Subject: Planned activities 1. SIAG OP-SF Summer Schools. The first of these was held at Laredo, Spain, July 24-28, 2000. Three more are planned: September 2001 in Germany, 2002 in Belgium, and 2003 in Portugal. Paco Marcellan and Walter Van Assche, our Program Director and Vice Chair, are leading the organizing committee for these events. 2. Sixth International Symposium on Orthogonal Polynomials, Special Functions, and Applications (OPSFA), Rome, Italy, June 18-22, 2001. The 7-member organizing committee includes 3 SIAG members (De Bruin, Marcellan, Muldoon). Of 8 invited speakers, 5 are SIAG members (Askey, Dunkl, Suslov, Temme, Van Assche). All SIAG officers will be present at this Symposium, and I plan to hold the 2001 officer's meeting there. Also, if additional SIAG members plan to be in Rome, please let me know in advance. If there are enough of us, it might be worthwhile to have a general member's meeting in Rome. 3. SIAM Annual Meeting, July 9-13, 2001. We have decided not to sponsor a minisymposium because recent annual meetings have not attracted our membership or, indeed, our officers. There are a variety of reasons for this, not least the existence each year of at least one meeting - and usually more than one - on orthogonal polynomials and special functions in the U.S. and abroad. Naturally, our members tend to use their limited travel budgets to attend meetings that are closely connected with their research. It doesn't help that our subject area has not been well-represented on the plenary programs at recent SIAM meetings. I am trying to open a dialog with SIAM about these problems. One idea is to ask SIAM to appoint a representative of our SIAG to be on the organizing committee for the 2002 annual meeting. This meeting will celebrate the 50th anniversary of SIAM in Philadelphia, the home city of SIAM. Another idea is SIAM/SIAG co-sponsorship of non-SIAM meetings. I hope further ideas will come from officers and members at the OPSFA meeting in Rome or by email to me. Topic #2 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: Daniel Lozier Subject: Request for Information for DLMF Project [This was sent to opsftalk on March 5, 2001] DLMF Editor's Note: The Web site for the DLMF (Digital Library of Mathematical Functions) is http://dlmf.nist.gov. For a long time the information there was very limited but that is beginning to change. Authors are writing chapters, and as these take shape details are being posted at the Web site. The DLMF will include selected typical applications of the various special functions, especially in physics. The following message from Dick Askey, a DLMF author as well as a DLMF Associate Editor, asks the readers of this list to help by providing examples. Please send them to opsftalk@nist.gov. For information about the OPSF-Talk List Service and access to the OPSF-Talk Archive, see http://math.nist.gov/opsf. I am general editor for the DLMF project. The other primary editors are Frank Olver (mathematics), Charles Clark (scientific applications), and Ron Boisvert (information technology). The associate editors are named at the Web site. Dan Lozier From: Richard Askey Subject: Request for information As many of you know, NIST is doing a revision of the Handbook of Mathematical Functions, now titled "The digital library of mathematical functions". In addition to including important facts about many special functions, there is a need to include references to uses of them. Each of us knows some, but collectively we know much more. It would be useful to the authors of the individual chapters if people sent examples of important uses of the usual special functions and their properties. Let me give an example of how an old handbook was used to suggest an interesting property of Legendre polynomials, and then mention a use of the inequalities which were suggested by one graph in Jahnke and Emde. When Legendre polynomials are graphed on (-1,1) a number of things are suggested. First, all the zeros lie in this interval. Second, the polynomials are bounded by 1 in absolute value on this interval. Third, if the absolute values of the successive extrema are considered, they decrease when going from 1 to 0. All of these facts had been observed and proved more than 100 years ago. About 55 years ago, John Todd looked carefully at a graph consisting of P_n(x) on (0,1) for n=1,2,...7. He noticed that the first minimum value of each of these functions when you look back from 1 seems to be an increasing function of n, the first maximum seems to be decreasing, and so on. These extrema have limits of the extrema of the Bessel function J_0(x). In a few years a proof was found by Gabor Szego, extended to ultraspherical polynomials suitably normalized by Otto Szasz, and a similar result was found for Hermite polynomials when suitably normalized. For many years these inequalities sat there as beautiful results but without serious use. The result for Legendre polynomials was rediscovered by Cornille and Martin in some work on pi-pi scattering. They also found a different weighted result for ultraspherical polynomials. Between the publication of their first paper and their second, someone told them of Szego's work. References are given in my SIAM regional conference lectures. It would have helped Cornille and Martin if this result had been included in a book they looked at. As we all know, results which are not eventually published in a book are very likely to get lost. Also, users of special functions will find it helpful to know the general areas in which these functions are used. Finally, mathematicians need to know about the uses of the functions since the users frequently need something just a little bit different than what mathematicians have done. There is another graph in Jahnke and Emde which was not looked at for even longer. This is a graph of Q_n(x) on (0,1) for n=1,2,3,4,5. A similar monotonicity result is suggested by this graph, and has been proven. I don't know applications of it, but strongly suspect there will be some. I am writing the chapters on gamma and beta functions and on higher hypergeometric series. Any references which can be sent about uses of these functions would be helpful. I am sure that the other authors would also find it useful to hear about applications of the functions they are writing about. To avoid duplication, it would be best to send them to the list opsftalk@nist.gov and Dan Lozier can forward them the author of the chapter if necessary. Thanks in advance for help. Dick Askey Topic #3 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor Subject: opsftalk After a quiet period, there has been here a recent spurt of activity in opsftalk, the discussion group of our Activity Group. Sergei Sadov asked whether certain formulas arising in matrices of potentials in the Legendre basis were known. Richard Askey pointed out a connection with work of Polya and Szego. George Gasper pointed out that another formulas asked about by Sadov is equivalent to a known formula of Whipple and Sadov forwarded further references sent to him by E. D. Krupnikov. David Strozzi asked about the numerical computation of the hypergeometric function bringing some responses and references from Daniel Lozier and Nico Temme. A remarkable aspect of these exchanges was the quick turnaround time. Readers are encouraged to subscribe and sent their questions and comments to opsftalk. See the end of Topic #16 for details. Topic #4 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: Erik Koelink Subject: Delft Workshop on Quantum Groups and Special Functions On Monday, April 9, 2001, there will be a one-day WORKSHOP `QUANTUM GROUPS AND SPECIAL FUNCTIONS' at the Technische Universiteit Delft. Programme: Hjalmar Rosengren (Goteborg, Sweden) Special functions and dynamical quantum groups Joris Van der Jeugt (Gent, Belgium) Character formulas of gl(m/n), Weyl's denominator formula and supersymmetric functions Stefaan Vaes (Leuven, Belgium) Extensions of locally compact quantum groups Johan Kustermans (Delft, the Netherlands) Quantum SU(1,1), yet another example of non-compact locally compact quantum group See http://aw.twi.tudelft.nl/~koelink/9april01.html for more information. Everybody is cordially invited. Topic #5 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: Paolo Emilio Ricci Subject: Workshop on Advanced Special Functions in Italy The 3rd Workshop on "Advanced Special Functions and Related Topics in Probability and in Differential Equations", will be held in Melfi (a small town in the South of Italy) in the period June 24-29, 2001. This Workshop is organized by Dr. G. Dattoli and C. Cesarano (ENEA - Frascati, Rome), Dr. D. Sacchetti and myself (Rome University "La Sapienza"). Prof. Dr. H.M. Srivastava (University of Victoria, Canada) will be a keynote speaker. If you are interested, you can take a look to the Internet page http://www.frascati.enea.it/melfi/ Please note that the total charge for participating will be around US $400, including the registration fee (US $200). This cost will cover the Hotel expenses (full board) for 5 days, coffee breaks, bus transportation from Rome to Melfi and vice-versa, the social dinner, and the Volume of Proceedings. If you are interested in spending some more days in Italy after the OPSFA Symposium, please contact me or another member of the Organizing Committee, and fill our "on line" registration form. The Workshop hotel (Parco Eudria) is far from Melfi, and located in a very quiet and nice place. An ideal place for relaxing and exchanging information after the OPSFA Symposium. Topic #6 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: Andre Ronveaux Subject: Benin Workshop on Mathematical Physics SECOND INTERNATIONAL WORKSHOP ON CONTEMPORARY PROBLEMS IN MATHEMATICAL PHYSICS INSTITUT DE MATHEMATIQUES ET DE SCIENCES PHYSIQUES (IMSP), PORTO-NOVO (BENIN). October 28th - November 2nd, 2001 The main objective of the workshop is to contribute to the development of a critical mass of researchers in Africa in such a dynamic area as mathematical physics. The workshop brings together specialists from diverse topics in Theoretical and Mathematical Physics. It offers to the international scientific community the possibility of exchanging useful information on contemporary problems in these fields through direct interaction. The workshop also provides young African researchers with an opportunity to know each other and to initiate scientific cooperation. Therefore the workshop helps to strengthen research capacity and revitalize activities in mathematical physics in African universities. Director: Professor M.N.Hounkonnou,(IMSP) Coordinators : J.P. Antoine, Université Catholique de Louvain, Louvain-la-Neuve(Belgium) H. Capo, Université Nationale du Bénin, Cotonou, (Benin) A. Msezane, Clark Atlanta University, Atlanta (USA) Topics include: Coherent States, Wavelets and Geometric Methods in Theoretical Physics Modern Physics; Field Theory, Atomic, Molecular, Statistical Physics and Theoretical Chemistry; Functional Analysis and Algebraic Methods for Theoretical Physics, Special Functions and Orthogonal Polynomials. The proceedings of the workshop will be published by World Scientific Publishing Co. The proceedings of the First International Workshop on Contemporary Problems in Mathematical Physics (COPROMAPH1) are available from the same publishing house. This second International workshop (COPROMAPH2) will be co-organized by Prof. J. Govaerts, Institut de Physique Nucléaire, Université Catholique de Louvain, 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgium, E-mail: govaerts@fynu.ucl.ac.be and Prof. M N Hounkonnou, Institut de Mathématiques et de Sciences Physiques (IMSP), B.P. 2628 Porto-Novo, Benin, E-mail: hounkon@syfed.bj.refer.org The activity is open to scientists from all countries. Travel and subsistence expenses of the participants should be covered by the home institution. However, limited funds will be made available for scientists from African countries. For more informations about: registration fees, presentation of communications, lodging facilities and the city of Cotonou please consult the web page http://www.chez.com/imspurpt/copromaph2 Topic #7 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor Subject: IMA Program on "Special Functions in the Digital Age" The Institute for Mathematics and its Applications, Minneapolis, Minnesota, USA, will host a summer Program "Special Functions in the Digital Age" in the period July 22 - August 2, 2002. The program is not yet open for registration and the schedule and list of participants are not yet available. The following description is taken form the web site: http://www.ima.umn.edu/digital-age/ Introduction: Mathematical tables and handbooks have played a pivotal role in applications and also the development of mathematics itself over the centuries. Now, with the advent of the digital age, the traditional handbook format has become obsolete, and a complete rethinking of the nature and role of mathematical handbooks must be undertaken. The purpose of this program is to formulate, though concrete examples and experiences, the role and character of digital libraries in mathematics, and the mathematical and applied fields that would benefit from such a library. The first serious attempt to address these issues is the ongoing Digital Library of Mathematical Functions (DLMF) project at the National Institute of Standards and Technology (NIST). This workshop will take the DLMF project as a basis for assessing both the state of the art in special function theory, what aspects are of importance in applications, particularly to chemistry and physics, and the experiences gained in this project to formulate recommendations for how digital libraries of mathematics should be organized, utilized, and developed. We also anticipate the experiences of the DLMF project to provide insight and recommendations for how mathematics should be stored and disseminated over the internet. Of the currently used handbooks, the most well-developed have been those devoted to special functions and their applications. The principal handbooks on special functions, "Higher Transcendental Functions" (the Bateman Project) and the NIST (formerly National Bureau of Standards) "Handbook of Mathematical Functions," are among the most useful, widely consulted technical volumes ever published, but they are now out of date, due to rapid research progress and revolutionary changes in technology. (See http://www.siam.org/siamnews/03-98/function.htm for additional information.) Using these as concrete examples of a mathematical digital library, the program will assess recent progress in updating these handbooks and recent advances in the theory and use of special functions, and to point out the areas of research in special functions that hold the most promise and importance for future development, both for theorists and users. In the broader arena, the workshop will aim to use the experience in this particular subject to generate recommendations for further digital library projects in the mathematical sciences and their applications, including, but not limited to, numerical analysis, group theory, signal processing, statistics, linear algebra, partial differential equations, and so on. Description: The IMA workshop will use the DLMF project as a foundation and discuss what more should be done, what areas are incomplete or unrepresented, what are the resulting mathematical, symbolic, numerical and web issues, applications in physics, chemistry, etc., relationships with the Bateman project, and potential for other digital libraries in other mathematical areas. The workshop is to have a very broad outlook, encompassing a wide range of subjects connected with special functions, as well as issues concerning digital libraries and the delivery of mathematics over the internet. A major portion of this program (7 days) will be assessments of research progress and promising vistas for future research by distinguished experts in the areas of asymptotics, combinatorial functions, statistics, computer algebra, algebraic and group theoretic methods, applications to the physical sciences, orthogonal polynomials, numerical methods, zeta functions & random matrices, Painlevé functions, elliptic functions, elliptic hypergeometric functions and the Heun function group, with the aim of pointing out what is of greatest importance in the theory and applications, and what should be included in digital library projects. The remainder of the program (3 days) will be devoted to Digital Libraries generally and, specifically, Digital Libraries and the Mathematical Sciences, including the delivery of mathematics over the Internet. It will conclude with a panel on the "Future of Mathematical Digital Libraries," with panelists from the special functions research and users communities, as well as representatives from mathematics societies and government funding agencies. There will be several discussion sessions to develop specific recommendations for special function topics to be included in future Digital Libraries in Mathematics. Also there will be poster sessions, and several software demonstrations (particularly of computer algebra and numerical packages for special functions), and much of the software will be available during the program for informal use by participants. This program will link with special function related sessions at the Foundations of Computational Mathematics (FoCM'02) meeting that will be hosted by the IMA, August 5-15, 2002. The program is meant for researchers in the theory and computation of special functions (definitely including people new to the field who are looking for the most promising areas for future research), for users of special functions, and for persons interested in the delivery of mathematics over the Internet. Topic #8 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: Anatoly Kilbas and Sergei Rogosin Subject: Report on AMADE-2001 International Conference "Analytical Methods of Analysis and Differential Equations" (AMADE-2001), Minsk, Belarus, February 15-19, 2001 The international conference "Analytical Methods of Analysis and Differential Equations" (AMADE-2001) took place February 15-19, 2001 in Minsk, Belarus. It continues the series of the international conferences "Boundary Value Problems, Special Functions and Fractional Calculus" devoted to the 90th birthday of academician F.D.Gakhov (Minsk, Belarus, February 15-20, 1996), and "Analytical Methods of Analysis and Differential Equations" (AMADE) (Minsk, Belarus, September 14-18, 1999). AMADE-2001 was organized by the Belarusian State University, the Belarusian National Academy of Sciences together with Moscow State University. It was held at the Olympic Sport Center "Staiki" which is situated 10 km from Minsk, the capital of Belarus. 262 mathematicians from 21 countries confirmed their interest in the Conference. Abstracts of their reports were published in "Abstracts of AMADE-2001". 138 scientists from Algeria, Belarus, France, Germany, Great Britain, Italy, Kasakhstan, Kuwait, Lithuania, Macedonia, Poland, Russia, Ukraine and Yugoslavia took part in AMADE-2001. The work of the conference was divided into four sections: 1. Integral transforms and special functions. 2. Differential equations and applications. 3. Integral, difference, functional equations and fractional calculus. 4. Real and complex analysis. There were 20 plenary invited lectures and 124 sectional talks devoted to different problems of analysis and differential equations. Plenary invited lectures were given by the following mathematicians: Antonevich A.B. (Minsk, Belarus) Homogeneous Banach algebras and algebraic fibering Begehr H. (Berlin, Germany) Orthogonal decompositions in $L_2$ Burenkov V.I. (Cardiff, UK) Equivalence of embedding theorems for Sobolev spaces to some spectral properties of Neumann Laplacian Volovich I.V. (Moscow, Russia), Radyno Ja.V. (Minsk, Belarus), Khrennikov À.Ju. (Vaxjo, Sweden) Operator of multiplication on the group of adels Vu Kim Tuan (Kuwait) The Paley-Wiener theorem for Sturm-Liouville transform Glaeske H.-J. (Jena, Germany) On a Hermite transform in spaces of generalized functions on $R^n$ Gromak V.I. (Minsk, Belarus) Discrete Painleve equations of the high order Dzhenaliev M.T., Ramazanov M.I. (Almaty, Kazakhstan) On loaded equations with periodic boundary conditions Galkowski K. (Z.Gora, Poland), Owens D.H. (Sheffield,UK) Control problems for a class of 2d repetitive systems Kakichev V.A. (Novgorod, Russia) Convolution of the Borel transform Karapetyants N.K. (Rostov-on-Don, Russia) On a statement of the problem for equations with fractional-linear shift on the axes Kilbas A.A. (Minsk, Belarus) Some aspects of the theory of differential and integral equations of fractional order Lanza de Cristoforis M., Lamberti P.D. (Padova, Italy) An analyticity theorem for symmetric functions of the eigenvalues of a compact self-adjoint operator Laurinchikas À. (Vilnius, Lituania) The universality of certain zeta function Marti J.-A. (Guadeloupe, France) On some characteristics of Cauchy problems Minyuk S.A. (Grodno, Belarus), Metelskii À.V. (Minsk, Belarus) On completeness of linear systems with a delay Mityushev V.V. (Slupsk, Poland) Problem of R-linear conjugation and its applications in mechanics of composite materials Rogosin S.V. (Minsk, Belarus) On complex variable approach for moving boundary value problems Yurchuk N.I., Baranovskaya S.N., Yashkin V.I. (Minsk, Belarus) On the classic and the weakened solutions of hyperbolic equations of even order February 19th, 2001 was a day in memory of academician F.D.Gakhov (1906-1980), the founder of Belarusian school on boundary value problems and singular integral equations. His former students and successors gave talks. Participants remarked on the high scientific level of the conference. The Proceedings of AMADE-2001 will be published in special issues of the Journal "Proceedings of Institute of Mathematics" of the Belarusian National Academy of Sciences. Some of the reports were recommended for publication in the Journal "Integral Transforms and Special Functions". Topic #9 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor Subject: Book by Dunkl and Xu on Orthogonal Polynomials of Several Variables [From the web site: http://www.cambridge.org] Title: Orthogonal Polynomials of Several Variables Authors: Dunkl, Charles and Xu, Yuan April 2001, 400 Pages, Hardback, ISBN: 0-521-80043-9, $80.00 This is the first modern book on orthogonal polynomials of several variables, which are valuable tools used in multivariate analysis, including approximations and numerical integration. The book presents the theory in elegant form and with modern concepts and notation. It introduces the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains such as the cube, the simplex, the sphere and the ball. It also focuses on those of Gaussian type, for which fairly explicit formulae exist. The authors' approach blends classical analysis and symmetry-group-theoretic methods. The book will be welcomed by research mathematicians and applied scientists, including applied mathematicians, physicists, chemists and engineers. SERIES NAME: Encyclopedia of Mathematics and its Applications SUBJECT: Mathematics - analysis, probability Topic #10 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor Subject: Book on Orthogonal Polynomial for Exponential Weights [From the Springer Mathematics Newsletter] Forthcoming: A.L. Levin, The Open University of Israel, Tel Aviv, and Doron S. Lubinsky, Witwatersrand University, Wits, South Africa Orthogonal Polynomial for Exponential Weights CMS Books in Mathematics, Vol 4 2000. Approx. 350 pp. Hardcover $69.95 (tent.) ISBN 0-387-98941-2 The analysis of orthogonal polynomials associated with general weights has been a major theme in classical analysis this century. The use of potential theory since the early 1980's has had a dramatic influence on the development of orthogonal polynomials associated with weights on the real line. For many applications of orthogonal polynomials, for example in approximation theory and numerical analysis, it is not asymptotics but certain bounds that are most important. In this monograph, the authors define and discuss their classes of weights, state several of their results on Christoffel functions, Bernstein inequalities, restricted range inequalities, and record their bounds on the orthogonal polynomials as well as their asymptotic results. This book will be of interest to researchers in approximation theory and potential theory, as well as in some branches of engineering. Topic #11 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor Subject: Book by Schoutens on Stochastic Processes and Orthogonal Polynomials [From the web site: http://www.springer-ny.com] Stochastic Processes and Orthogonal Polynomials Series: Lecture Notes in Statistics, Vol. 146 Wim Schoutens, Katholieke Universiteit Leuven, B-3001 Heverlee Price $49.95 184 pages , 6 1/8 x 9 1/4, paperback ISBN: 0-387-95015-X, published 2000 ABOUT THIS BOOK The book offers an accessible reference for researchers in the probability, statistics and special functions communities. It gives a variety of interdisciplinary relations between the two main ingredients of stochastic processes and orthogonal polynomials. It covers topics like time dependent and asymptotic analysis for birth-death processes and diffusions, martingale relations for Levy processes, stochastic integrals and Stein's approximation method. Almost all well-known orthogonal polynomials, which are brought together in the so-called Askey Scheme, come into play. This volume clearly illustrates the powerful mathematical role of orthogonal polynomials in the analysis of stochastic processes and is made accessible for all mathematicians with a basic background in probability theory and mathematical analysis. Wim Schoutens is a Postdoctoral Researcher of the Fund for Scientific Research-Flanders (Belgium). He received his PhD in Science from the Catholic University of Leuven, Belgium. Topic #12 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor Subject: Further information on the Hong Kong Proceedings [This is from information sent by Charles Dunkl and Dan Lozier] In connection with the Proceedings of the International Workshop on Special Functions -- Asymptotics, Harmonic Analysis and Mathematical Physics held June 21-25, 1999 at the City University of Hong Kong, the following is the full bibliographic information to supplement our announcement in OP-SF NET 7.6, Topic #5 : Special Functions: Proceedings of the International Workshop, C. Dunkl, M. Ismail, R. Wong, editors, 438 + xi pages, World Scientific (Singapore), ISBN 981-02-4393-6, 2000. There was a panel discussion at the Workshop, for which a summary was written. This summary is mentioned in the preface to the Proceedings but was omitted inadvertently. It can be seen at http://math.nist.gov/opsf/books/hongkong99.html. It appeared also in OPSF-NET 6.5, Topic # 7 (September 1999) and in the printed Newsletter (vol. 10, no. 1, October 1999). For further information about the Workshop, including photographs, see http://www.cityu.edu.hk/ma/conference/iwsf/index.html. Topic #13 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: Wolfram Koepf Subject: Maple packages for hypergeometric summation Updates of the Maple packages hsum.mpl and qsum.mpl for hypergeometric summation and q-hypergeometric summation [see my book "Hypergeometric Summation", Vieweg, Braunschweig, 1988, distributed in the North America by the AMS, see http://www.ams.org/bookstore, reviewed in OP-SF NET 6.4 #12] can be obtained from the web page http://www.mathematik.uni-kassel.de/~koepf/Publikationen. The updates work now with Maple V and Maple 6, and the names of the updated versions are hsum6.mpl and qsum6.mpl. They contain implementations of Gosper's, Zeilberger's and Petkovsek's algorithms and their corresponding q-versions. Topic #14 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor Subject: OP-SF preprints in xxx archive The following preprints related to the fields of orthogonal polynomials and special functions were recently posted or cross-listed to one of the subcategories of the xxx archives. See especially: http://front.math.ucdavis.edu/math.CA http://front.math.ucdavis.edu/math.CO http://front.math.ucdavis.edu/math.QA http://xxx.lanl.gov/archive/solv-int math.RT/0101006 Title: A generating function for the trace of the Iwahori-Hecke algebra Authors: Eric M. Opdam Subj-class: Representation Theory MSC-class: 20C08, 22D25, 22E35 math.RT/0101007 Title: On the spectral decomposition of affine Hecke algebras Authors: Eric M. Opdam Subj-class: Representation Theory MSC-class: 20C08, 22D25, 22E35, 43A32 math.CA/0101011 Title: Some divergent trigonometric integrals Authors: Erik Talvila Comments: to appear in a slightly different version in Amer. Math. Monthly Subj-class: Classical Analysis MSC-class: 26A42 math.CA/0101012 Title: Necessary and sufficient conditions for differentiating under the integral sign Authors: Erik Talvila Subj-class: Classical Analysis MSC-class: 26A39 math.CA/0101013 Title: Rapidly growing Fourier integrals Authors: Erik Talvila Subj-class: Classical Analysis MSC-class: 42A math.CA/0101065 Title: Bessel Integrals and Fundamental Solutions for a Generalized Tricomi Operator Authors: J. Barros-Neto, Fernando Cardoso Subj-class: Classical Analysis; Analysis of PDEs MSC-class: 35M10 (primary) 46F10, 42B10 (secondary) math.CA/0101073 Title: A proof of a multivariable elliptic summation formula conjectured by Warnaar Authors: Hjalmar Rosengren Comments: 10 pages Subj-class: Classical Analysis; Quantum Algebra MSC-class: 33D67; 33E05 math.CA/0101105 Title: Orthogonal Polynomials in Analytical Method of Solving Differential Equations Describing Dynamics of Multilevel Systems Authors: V.A.Savva, V.I.Zelenkov, A.S.Mazurenko Comments: 8 pages, latex, no figures, see also this http URL and this http URL Subj-class: Classical Analysis; Dynamical Systems MSC-class: 33C48; 34C25 Journal-ref: Integral Transforms and Special Functions, 2000, Vol. 10, No. 3--4, pp. 299-308 math.AP/0101113 Title: Fundamental Solutions for the Tricomi Operator, II Authors: J. Barros-Neto, Israel M. Gelfand Subj-class: Analysis of PDEs; Classical Analysis MSC-class: 35M10; 33C05 math.CA/0101125 Title: Duality of orthogonal polynomials on a finite set Authors: Alexei Borodin Comments: AMSTeX, 9 pages Subj-class: Classical Analysis; Probability Theory math.QA/0101136 Title: Special functions, conformal blocks, Bethe ansatz, and SL(3,Z) Authors: G. Felder, A. Varchenko Comments: 10 pages, AMSLaTeX Subj-class: Quantum Algebra; Mathematical Physics MSC-class: 81T40; 33C67 math.CA/0101168 Title: On the sums Sum((4k+1)^(-n),k,-inf,+inf) Authors: Noam D. Elkies Comments: 13 pages. Written partly as an expository paper, and thus at somewhat greater length than would be appropriate for a purely research article on this material. Revised to correct minor errors: typos in equations (1) and (2), and an incomplete argument for Lemma 2, noticed respectively by Paul Krapivsky and Robin Chapman Subj-class: Classical Analysis; Combinatorics MSC-class: 11B68 (Primary) 05A15 (Secondary) math.QA/0101178 Title: q-Analogues for Green functions for powers of the invariant Laplacian in the unit disc Author: D. Shklyarov Comments: LaTeX 2e, 18 pages, vaksman@ilt.kharkov.ua Subj-class: Quantum Algebra; Complex Variables; Functional Analysis MSC-class: 81R50 (Primary) 81Q99 (Secondary) Journal-ref: Mathematical physics, analysis, geometry (Kharkov Mathematical Journal), v.7, 2000, p.345-365 math.CA/0101187 Title: Little q-Legendre polynomials and irrationality of certain Lambert series Authors: Walter Van Assche Comments: 15 pages Subj-class: Classical Analysis; Number Theory MSC-class: 33D45; 11J82 math.CA/0101188 Title: Multiple orthogonal polynomials associated with Macdonald functions Authors: W. Van Assche, S.B. Yakubovich Comments: 13 pages Subj-class: Classical Analysis MSC-class: 33C10; 42C05 Journal-ref: Integral Transforms and Special Functions 9 (2000), 229-244 math.QA/0101216 Title: Generalized Hermite polynomials Author: Vadim V. Borzov Comments: 15 pages, no figures Subj-class: Quantum Algebra; Classical Analysis MSC-class: 05E35 (Primary) 05E35 (Secondary) math.QA/0101259 Title: The integral representations of the q-Bessel-Macdonald functions Authors: V.-B.K. Rogov Comments: 10 pages, Latex Subj-class: Quantum Algebra MSC-class: 22Exx cond-mat/0101464 Title: Solution of a Generalized Stieltjes Problem Authors: B. Sriram Shastry, Abhishek Dhar Comments: 19 pages, 4 figures Subj-class: Condensed Matter; Exactly Solvable and Integrable Systems; Mathematical Physics; Classical Analysis math.GM/0102031 Title: Riemann hypothesis and Superconformal Invariance Authors: Matti Pitkanen Comments: 17 pages, addition of new material about realization of superconformal symmetry Subj-class: General Mathematics math.CA/0102032 Title: Analytic continuation of the generalized hypergeometric series near unit argument with emphasis on the zero-balanced series Authors: Wolfgang Buehring, H. M. Srivastava Comments: 19 pages Subj-class: Classical Analysis MSC-class: 33C20, 34E05 (Primary) 41A58 (Secondary) Journal-ref: Themistocles M. Rassias (Editor), Approximation Theory and Applications, Hadronic Press, Palm Harbor, FL 34682-1577, U.S.A., ISBN 1-57485-041-5, 1998, pp. 17-35 math.CO/0102073 Title: Variants of the Andrews-Gordon Identities Authors: A. Berkovich, P. Paule Comments: 12 pages, 1 figure Subj-class: Combinatorics; Number Theory; Quantum Algebra MSC-class: 05A10, 05A19, 11B65, 11P82 math.CO/0102106 Title: A computer proof of a polynomial identity implying a partition theorem of Goellnitz Authors: A. Berkovich, A. Riese Comments: 12 pages, to appear in Adv. Appl. Math Subj-class: Combinatorics; Number Theory; Quantum Algebra MSC-class: 05A19, 05A30, 11P82, 33F10 math.CA/0102111 Title: Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms Authors: Aline Bonami, Bruno Demange, Philippe Jaming Comments: 22 pages, submitted Subj-class: Classical Analysis; Mathematical Physics MSC-class: 42B10;32A15;94A12 hep-th/0102039 Title: A_N-type Dunkl operators and new spin Calogero-Sutherland models Authors: F. Finkel, D. Gomez-Ullate, A. Gonzalez-Lopez, M.A. Rodriguez, R. Zhdanov Comments: 18 pages. Typeset using LaTeX with amslatex and revtex 4 packages Subj-class: High Energy Physics - Theory; Mathematical Physics; Exactly Solvable and Integrable Systems math-ph/0102007 Title: On the Motion of Zeros of Zeta Functions Authors: Hans Frisk, Serge de Gosson Comments: 11 pages, 3 figures (better image resolution available on this http URL) Subj-class: Mathematical Physics MSC-class: 11M06 math-ph/0102020 Title: Laplace transform of spherical Bessel functions Authors: A. Ludu, R. F. O'Connell Comments: 5 pages LATEX, no figures Subj-class: Mathematical Physics; Algebraic Geometry math-ph/0102026 Title: The Darboux Transform and some Integrable cases of the q-Riccati Equation Authors: A. Odzijewicz, A. Ryzko Comments: 11 pages LATEX Subj-class: Mathematical Physics nlin.SI/0101056 Title: A Determinant Formula for a Class of Rational Solutions of Painlev\'e V Equation Authors: Tetsu Masuda, Yasuhiro Ohta, Kenji Kajiwara Comments: 17 pages Subj-class: Exactly Solvable and Integrable Systems nlin.SI/0102020 Title: Special Functions of the Isomonodromy Type, Rational Transformations of Spectral Parameter, and Algebraic Solutions of the Sixth Painlev\'e Equation Author: A. V. Kitaev Comments: 13 pages Subj-class: Exactly Solvable and Integrable Systems hep-th/0102180 Title: Unitary representations of $U_{q}(\mathfrak{sl}(2,\RR))$, the modular double, and the multiparticle q-deformed Toda chains Authors: S. Kharchev, D. Lebedev, M. Semenov-Tian-Shansky Comments: AmsLatex, 41 pages, 3 figures Subj-class: High Energy Physics - Theory; Quantum Algebra; Exactly Solvable and Integrable Systems Topic #15 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor Subject: Changes of Address, WWW pages, etc. Grigori Olshanski writes to inform us that his private email address olsh@glasnet.ru will be cancelled soon. Please note the new address: olsh@online.ru You can also use his official address olsh@iitp.ru Topic #16 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor Subject: About the Activity Group The SIAM Activity Group on Orthogonal Polynomials and Special Functions consists of a broad set of mathematicians, both pure and applied. The Group also includes engineers and scientists, students as well as experts. We have around 140 members scattered about in more than 20 countries. Whatever your specialty might be, we welcome your participation in this classical, and yet modern, topic. Our WWW home page is: http://math.nist.gov/opsf/ This is a convenient point of entry to all the services provided by the Group. Our Webmaster is Bonita Saunders (bonita.saunders@nist.gov). The Activity Group sponsors OP-SF NET, which is transmitted periodically by SIAM. It is provided as a free public service; membership in SIAM is not required. The OP-SF Net Editor is Martin Muldoon (muldoon@yorku.ca). To receive the OP-SF NET, send your name and email address to poly-request@siam.org. Back issues can be obtained at the WWW addresses: http://turing.wins.uva.nl/~thk/opsfnet http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html http://math.nist.gov/opsfnet/archive The NET provides fast turnaround compared to the printed Newsletter, also sponsored by the Activity Group, and edited by Renato Alvarez-Nodarse and Rafael Yanez. It appears three times a year and is mailed by SIAM. Back issues are accessible at: http://www.mathematik.uni-kassel.de/~koepf/siam.html To receive the Newsletter, you must be a member of SIAM and of the Activity Group. SIAM has several categories of membership, including low-cost categories for students and residents of developing countries. For current information on SIAM and Activity Group membership, contact: Society for Industrial and Applied Mathematics 3600 University City Science Center Philadelphia, PA 19104-2688 USA phone: +1-215-382-9800 email: service@siam.org WWW : http://www.siam.org http://www.siam.org/membership/outreachmem.htm Finally, the Activity Group operates an email discussion group, called OP-SF Talk. To subscribe, send the email message subscribe opsftalk Your Name to listproc@nist.gov. To contribute an item to the discussion, send email to opsftalk@nist.gov. The archive of all messages is accessible at: http://math.nist.gov/opsftalk/archive Topic #17 ------------ OP-SF NET 8.2 ---------------- March 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor Subject: Submitting contributions to OP-SF NET and Newsletter To contribute a news item to OP-SF NET, send email to poly@siam.org with a copy to the OP-SF Editor . Please note that submissions to the Net are automatically considered for the Newsletter, and vice versa, unless the contributor requests otherwise. Contributions to the OP-SF NET 8.3 should be sent by May 1, 2001. Please send your (printed) Newsletter contributions directly to the Editors: Renato Alvarez-Nodarse Departamento de Analisis Matematico Universidad de Sevilla Apdo. Postal 1160, Sevilla E-41080 Spain fax: +34-95-455-7972 e-mail: renato@gandalf.ugr.es ran@cica.es Rafael J. Yanez Departamento de Matematica Aplicada Universidad de Granada E-18071 Granada, Spain phone: +34-58-242941 fax: +34-58-242862 e-mail: ryanez@ugr.es preferably by email, and in latex format. Other formats are also acceptable and can be submitted by email, regular mail or fax. The deadline for submissions to be included in the June 2001 issue is May 15, 2001 and for the October 2001 issue it is September 15, 2001. 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 Subscribe by mailing to: poly-request@siam.org or to: listproc@nist.gov Get back issues from URL: http://turing.wins.uva.nl/~thk/opsfnet/ WWW home page of this Activity Group: http://math.nist.gov/opsf/ Information on joining SIAM and this activity group: service@siam.org o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o The elected Officers of the Activity Group (1999-2001) are: Daniel W. Lozier, Chair Walter Van Assche, Vice Chair Charles F. Dunkl, Secretary Francisco Marcellan, Program Director The appointed officers are: Renato Alvarez-Nodarse and Rafael J. Yanez, Newsletter Editors Martin Muldoon, OP-SF NET editor Bonita Saunders, Webmaster o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o