o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - - - February 3, 1994 - - O P - S F N E T Volume 1, Number 2 - - ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - - Tom H. Koornwinder, Editor thk@fwi.uva.nl - - - - - - The Electronic News Net of the SIAM Activity Group - - on Orthogonal Polynomials and Special Functions - - - - Please send contributions to: poly@siam.org - - & address changes to: poly-request@siam.org - - - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o Today's Topics: 1. Back issues of OP-SF Net archived 2. Submission deadlines for next issues of OP-SF Net and Newsletter 3. Activity on Representation Theory and q-Special Functions (second announcement) 4. Minisymposium "Special Functions and Asymptotics" (second announcement) 5. Workshop on Transform Methods and Special Functions (second announcement) 6. Special functions conference at Sam Houston State University 7. Thomas Stieltjes Conference, Delft, 1994 (second announcement) 8. New book on generalized fractional calculus 9. Question about closed form for an integral 10. Question about OP's with coefficients in a finite field 11. Historical remark about Stieltjes and Meixner polynomials 12. Anonymous ftp site on Orthogonal Polynomials etc. Topic #1 -------------- OP-SF NET --------------- February 3, 1994 ~~~~~~~~~ From: Tom H. Koornwinder Subject: Back issues of OP-SF Net archived Back issues of OP-SF Net can be obtained from SIAM's anonymous FTP server, internet address ae.siam.org , in directory pub/opsf-net . Topic #2 -------------- OP-SF NET --------------- February 3, 1994 ~~~~~~~~~ From: Tom H. Koornwinder Subject: Submission deadlines for next issues of OP-SF Net and Newsletter Contributions to the third issue of OP-SF Net should reach the email address poly@siam.org before March 16, 1994. Contributions to the Spring issue of the Orthogonal Polynomials and Special Functions Newsletter should reach the Editor Eugene Tomer before February 11, 1994. The preferred mode is a Latex file sent to his email address etomer@netcom.com . Alternatively, or in addition, send hard copy to: Eugene Tomer Applied Mathematics & Computing 150 Hernandez Avenue San Francisco, CA 94127, USA fax +1-415-731 3551 Contributions to either the Net or to the Newsletter will be automatically considered also for inclusion in the other medium. Topic #3 -------------- OP-SF NET --------------- February 3, 1994 ~~~~~~~~~ From: Tom H. Koornwinder Subject: Activity on Representation Theory and q-Special Functions (second announcement) The Thomas Jan Stieltjes Research Institute is a newly-organized inter-university mathematical research center which is physically spread over the mathematics departments of the participating universities in the western part of The Netherlands. Within the framework of the Institute's program there will be a period of concentration on representation theory and q-special functions. Thus, between April and June, 1994, a number of guests are expected, for a longer or shorter time, short courses will be given on graduate level, and weekly seminars will be held. The focus will be on Heckman-Opdam hypergeometric functions associated with root systems, and interpretations of Macdonald's orthogonal $q$-polynomials on quantum groups. The activity will take place both at the Universities of Leiden and Amsterdam. The following three guests will stay for at least one month and will give short courses: - Ian G. Macdonald (London, England), May, "Affine Hecke algebras and orthogonal polynomials" - Charles F. Dunkl (Charlottesville, Virginia, USA), half of April - end of May, "Special Functions, Coxeter Groups, and Differential-Difference Operators" - Masatoshi Noumi (Tokyo, Japan), half of April - half of June, "Quantum Gelfand pairs related to Macdonald polynomials" In a next announcement the full list of guests will be given. Further information can be obtained from Tom Koornwinder (thk@fwi.uva.nl) or from Eric Opdam (opdam@rulcri.leidenuniv.nl). Topic #4 -------------- OP-SF NET --------------- February 3, 1994 ~~~~~~~~~ From: Martin Muldoon Subject: Minisymposium "Special Functions and Asymptotics" (second announcement) At the SIAM Annual Meeting, San Diego, July 25-29, 1994, Charles F. Dunkl ( University of Virginia) and Martin Muldoon, (York University, Canada) will organize a minisymposium on "Special Functions and Asymptotics". It is cosponsored by the SIAM Activity Group on Orthogonal Polynomials and Special Functions. Description: Many problems arising in the natural sciences, engineering, combinatorics, statistics, etc. lead ultimately to approximating integrals or solving differential equations. The two topics of this minisymposium describe the basic solutions and techniques required to deal with such problems. All but the simplest special functions are often best described by asymptotic information (typically as one or more of the variables approaches infinity); at the same time, the asymptotic behavior of complicated functions is often best understood through the medium of known special functions. Frank Olver's classic "Asymptotics and Special Functions" (Academic Press, 1974) stresses this duality. This minisymposium will explore a variety of current approaches in these classical subjects. Speakers: Richard Askey, University of Wisconsin Title: "Extensions of Hermite polynomials and other orthogonal polynomials" Bruce Berndt, University of Illinois Title: "Some asymptotic formulas of Ramanujan" T.M. Dunster, San Diego State University Title: "New uniform asymptotic approximations for Jacobi polynomials" Ronald Evans, University of California at San Diego Title: "Multidimensional q-beta integrals" George Gasper, Northwestern University Title: "Applications of sums and integrals of squares of special functions" Jeffrey S. Geronimo, Georgia Institute of Technology Title: "Asymptotics and spectral properties of orthogonal polynomials based on their recurrence coefficients" Adri Olde Daalhuis, University of Maryland Title: "Hyperasymptotics" Andre Ronveaux, FUNDP, Namur, Belgium Title: "Heun's equations and the Schroedinger equation" Renato Spigler, University of Padua. Italy Title: "Discrete Liouville-Green approximations and orthogonal polynomial asymptotics" Frank Stenger, University of Utah Title: "Asymptotics methods complemented by numerical methods" Audrey Terras, University of California at San Diego Title: "Comparison of special functions for finite and continuous symmetric spaces" Get information about registration for the SIAM annual meeting and about the further program of the meeting by sending email to meetings@siam.org . For further information about the minisymposium please contact Martin Muldoon (muldoon@nexus.yorku.ca). Topic #5 -------------- OP-SF NET --------------- February 3, 1994 ~~~~~~~~~ From: Virginia Kiryakova Subject: Workshop on Transform Methods and Special Functions (second announcement) Workshop on Transform Methods and Special Functions Sofia, Bulgaria, 12-17 August, 1994 Main subjects of the Workshop are: Integral Transforms, Special Functions, Series Expansions, Fractional Calculus and Generalizations, Algebraical Analysis, Operational Calculus, Applications to Complex Analysis, Differential and Integral Equations. Organizing Committee: P. Rusev, I. Dimovski and S.L. Kalla (chairmen), V. Kiryakova and L. Boyadjiev (secretaries). Place: Resort Town of Bankya, 20 km from Sofia. Full Board: for all the period (lodgings, breakfast, lunch and supper) approx. USD 150. Participation Fee: USD 100 (for accompanying persons: USD 50). Deadline: Since the necessary number of rooms and halls in hotel "Journalist" should be booked long in advance, those who wish to participate are kindly asked to contact as soon as possible via E-mail or Fax: Assoc. Prof. V. Kiryakova, Institute of Mathematics Bulgarian Academy of Sciences, Sofia 1090, Bulgaria fax: +359-2-752 078, e-mail: virginia@bgearn.bitnet Topic #6 -------------- OP-SF NET --------------- February 3, 1994 ~~~~~~~~~ From: Patrick J. Van Fleet Subject: Special functions conference at Sam Houston State University This is an announcement for a possible National Conference on Special Functions and their Applications --- contingent upon funding --- at Sam Houston State University from August 25 - 27, 1994. Sam Houston State University is located in Huntsville, Texas, approximately 65 miles north of Houston. This proposed national conference is intended to provide a forum for the exchange of new ideas and techniques from several areas of special function theory and its applications. The following mathematicians have tentatively agreed to speak: G. Andrews, Penn State University R. Askey, University of Wisconsin B. C. Carlson, Iowa State University - Ames Lab J. Dickey, University of Minnesota R. Gustafson, Texas A&M University E. Neuman, Southern Illinois Unversity V. Retakh, Harvard University R. Wong, University of Manitoba. The list of these main speakers is indicative of the wide range of topics to be covered by this proposed conference. If you are interested in attending and/or contributing a paper to this proposed national conference, please let us know and we will put you on our mailing list and keep you updated. If you would, please indicate if you are interested in contributing a talk and/or a paper for the proceedings. We encourage graduate students to participate and contribute to this proposed conference. Our addresses are: Patrick J. Van Fleet Peter R. Massopust Department of Mathematics Department of Mathematics Sam Houston State University Sam Houston State University Huntsville, TX 77341, USA Huntsville, TX 77341, USA tel. +1-409-294 1493 tel. +1-409-294 1493 email mth_pvf@shsu.edu email mth_prm@shsu.edu Topic #7 -------------- OP-SF NET --------------- February 3, 1994 ~~~~~~~~~ From: Marcel G. de Bruin Subject: Thomas Stieltjes Conference, Delft, 1994 (second announcement) A first announcement of the conference "Orthogonality, Moment Problems and Continued Fractions", an international conference in honour of Thomas Jan Stieltjes Jr. (1856-1894), October 31 - November 4, 1994, Delft University of Technology, The Netherlands appeared in OP-SF Net 1.1. A second announcement, including a registration form, has gone out now. It can be obtained by sending a request to email address tjs94@twi.tudelft.nl . From the second announcement the following information is extracted here. Registration: before May 1, 1994 Short communications: If you want to contribute a short communication (about 20 minutes), please send an abstract (two pages A4 at most) before May 1, 1994. Proceedings: The Proceedings of the conference will be published as a special issue of the Journal of Computational and Applied Mathematics. Manuscripts must be submitted in triplicate during (or before) the conference. Conference fees: The conference fees are Dfl. 600 for participants, including the program and book of abstracts, a copy of the proceedings, all lunches and dinners, coffee, tea and an excursion. Invited lectures: C. Berg : Indeterminate moment problems and the theory of entire functions G. van Dijk : Thomas Jan Stieltjes : mathematician by profession? J.B. Hiriart-Urruty : Differentiability and non-differentiability in mathematical problems L. Lorentzen : Continued fractions F. Marcellan : Differential-difference operators and orthogonal polynomials in Sobolev spaces P. Nevai : Generalized polynomials F. Peherstorfer : Stieltjes polynomials and Gauss-Kronrod quadrature N.M. Temme : Current problems in uniform asymptotic estimates of integrals W. Van Assche : The impact of Stieltjes' work on orthogonal polynomials Further information: TJS94, Room H4.11 Department of Pure Mathematics Delft University of Technology P.O. Box 5031 2600 GA Delft The Netherlands email: tjs94@twi.tudelft.nl Topic #8 -------------- OP-SF NET --------------- February 3, 1994 ~~~~~~~~~ From: Virginia Kiryakova Subject: New book on generalized fractional calculus The following book appeared: Virginia Kiryakova Generalized Fractional Calculus and Applications Pitman Research Notes in Mathematics Ser., No 301 Longman Scientific & Technical ISBN 0-582-21977-9, 42,50 pound for USA and Canada: John Wiley & Sons, ISBN 0-470-23376-1 Readership: Mathematicians concerned with Fractional Calculus, Special Functions and Integral Transforms, Differential and Integral Equations, Operational and Convolutional Calculus, Analytic Functions and users of Applied Analysis. Abstract: The book is devoted to a systematic and unified development of a new Generalized Fractional Calculus, related to many special cases (most of the generalized integrals and derivatives introduced by different authors) and various applications. The basic operators are the generalized (multiple Erdelyi-Kober) fractional integrals and derivatives defined by means of convolutional integrals whose kernels are Meijer's G-functions, or Fox's H-functions. Their basic properties are derived and various applications are discussed, in particular to: the hyper-Bessel differential operators and ODE-s, Gelfond-Leontiev operators, generalized Laplace type integral transforms, operational and convolutional calculi, special functions of hypergeometric type and their new representations, solutions to classes of differential and integral equations, transmutation method, etc. To make the exposition self-contained an Appendix is included, dealing with the special functions used in the book. Contents: Introduction; Chapter 1. Generalized operators of fractional integration and differentiation; Chapter 2. Recent aspects of Erdelyi-Kober operators; Chapter 3. Hyper-Bessel differential and integral operators and equations; Chapter 4. Applications to generalized hypergeometric functions; Chapter 5. Further generalizations and applications; Appendix. Definitions, examples and properties of the special functions used in the book; References; Citation Index; 400 p. Author's address: Assoc. Prof. Dr. Virginia Kiryakova, Institute of Mathematics, Bulgarian Academy of Sciences, P.O. Box 373, Sofia 1090, Bulgaria email: virginia@bgearn.bitnet Enquiries and orders (except for USA and Canada): Judy Higgins, Longman Higher Education, Longman House, Burnt Mill, Harlow, Essex CM20 2JC, England (Fax: +44-279-623 862) For USA and Canada: Beth Schacht, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, USA Topic #9 -------------- OP-SF NET --------------- February 3, 1994 ~~~~~~~~~ From: Paul Abbott Subject: Question about closed form for an integral Suggestions for a closed form solution to the following problem appreciated. S / | u Defining H[S] = | [e - 1] du | ----------- / u 0 = Sum[S^n / (n n!), {n,1,Infinity}] = ExpIntegralEi[S] - Log[S] - EulerGamma Then Integrate[E^(-R y) H[S (1 - y)], {y, -1, 1}] R -R e H[2S] - e {H[2S+2R] - H[2R]} = --------- ----------------------- R R I am trying to find a closed form expression for the following integral: Integrate[E^(-R y) H[S (1 - y)] H[T (1 + y)], {y, -1, 1}] Any pointers or references to integrals of this type would be greatly appreciated. Paul Abbott Department of Physics Nedlands 6009 Phone: +61-9-380 2734 Fax: +61-9-380 1014 email: paul@earwax.pd.uwa.edu.au Topic #10 ------------- OP-SF NET --------------- February 3, 1994 ~~~~~~~~~ From: Herve LeFerrand (via Alphonse P. Magnus) Subject: Question about OP's with coefficients in a finite field Herve LeFerrand wishes to know if something has been done on OP's with coefficients in a finite field. Any tip? Topic #11 ------------- OP-SF NET --------------- February 3, 1994 ~~~~~~~~~ From: Galliano Valent Subject: Historical remark about Stieltjes and Meixner polynomials In the next issue of the Orthogonal Polynomials and Special Functions Newsletter a one-page note by Galliano Valent will appear with the title "Stieltjes results on Meixner polynomials". The paper makes clear that Stieltjes had obtained the explicit form of the orthogonality measure for Meixner polynomials already in 1895, roughly fourty years before Meixner published his paper on these polynomials. For further information, read the Newsletter or contact: Galliano Valent Laboratoire de Physique Theorique et des Hautes Energies Unite associee au CNRS URA 280 Universite Paris 7 2 Place Jussieu 75251 Paris Cedex 05, France email: valent@lpthe.jussieu Topic #12 ------------- OP-SF NET --------------- February 3, 1994 ~~~~~~~~~ From: Waleed A. Al-Salam Subject: Anonymous ftp site on Orthogonal Polynomials etc. Waleed Al-Salam has an anonymous ftp site at euler.math.ualberta.ca on orthogonal polynomials and related special functions. Manuscripts can be obtained from directory pub and subdirectories. In particular, examine the CONTENTS file in the pub directory. If you wish to receive periodic info regarding recent additions to this database please send an email message to waleed@euler.math.ualberta.ca with your e-mail address. You are invited to submit one or more of your not-yet-in-print manuscripts which you wish to make available to the general OPS community. They should be in Plain TeX, Latex, AMSTeX or AMSLaTeX format. These manuscripts can be submitted by one of the following methods: a) E-mail to waleed@EULER.MATH.UALBERTA.CA b) anonymous ftp to euler.math.ualberta.ca then "cd submissions" and finally "put file" where "file" is the name of the file you wish to deposit. o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - OP-SF Net is a forum of the SIAM Activity Group on - - Special Functions and Orthogonal Polynomials. - - We disseminate your contributions on anything of interest to the - - special functions and orthogonal polynomials community. This - - includes announcements of conferences, forthcoming books, new - - software, electronic archives, research questions, job openings. - - Submissions with sufficiently long useful life will also be - - considered automatically for our quarterly printed newsletter. - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - Send submissions to: poly@siam.org - - Send address changes to: poly-request@siam.org - - Get back issues by anonymous ftp from: ae.siam.org - - (directory pub/opsf-net) - - Information on joining SIAM - - and this activity group: service@siam.org - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - The Officers of the Activity Group are: - - - - Charles Dunkl, Chair - - George Gasper, Vice Chair - - Tom H. Koornwinder, Secretary - - Martin E. Muldoon, Program Director - - Eugene Tomer, Newsletter Editor - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o