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Summation Theorems for Basic Hypergeometric Series of Schur Function Argument

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Book cover Progress in Approximation Theory

Part of the book series: Springer Series in Computational Mathematics ((SSCM,volume 19))

Abstract

In this paper we prove a Ramanujan 1 ψ 1 summation theorem for a Laurent series extension of I.G. Macdonald’s (Schur function) multiple basic hypergeometric series of matrix argument. This result contains as special, limiting cases our Schur function extension of the q-binomial theorem and the Jacobi triple product identity. Just as in the classical case, we write our new q-binomial theorem and 1 ψ 1 summation as elegant special cases of K. Kadell’s and R. Askey’s q-analogs of Selberg’s multiple beta-integral. We also apply our q-binomial theorem and K. Kadell’s Schur function q-analog of Selberg’s beta-integral to derive a Heine transformation and q-Gauss summation theorem for Schur functions.

Partially supported by joint NSF/NSA grant DMS-8904455.

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Authors and Affiliations

  1. Department of Mathematics, Ohio State University, 231 West 18th Ave, 43210, Columbus, OH, USA

    S. C. Milne

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  1. S. C. Milne
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Editors and Affiliations

  1. Steklov Mathematics Institute, 117966, Moscow GSP-1, Russia

    A. A. Gonchar

  2. Institute for Constructive Mathematics, University of South Florida, 33620, Tampa, FL, USA

    E. B. Saff

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© 1992 Springer-Verlag New York, Inc.

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Milne, S.C. (1992). Summation Theorems for Basic Hypergeometric Series of Schur Function Argument. In: Gonchar, A.A., Saff, E.B. (eds) Progress in Approximation Theory. Springer Series in Computational Mathematics, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2966-7_3

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  • DOI: https://doi.org/10.1007/978-1-4612-2966-7_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7737-8

  • Online ISBN: 978-1-4612-2966-7

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