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Some Extensions of the Beta Integral and the Hypergeometric Function

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Orthogonal Polynomials

Part of the book series: NATO ASI Series ((ASIC,volume 294))

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Abstract

This is a brief survey of the theory of basic hypergeometric series with particular emphasis on some extensions of Euler’s beta integral and Gauss’ hypergeometric function. From Heine’s q-analogue of the binomial theorem we develop the summation and transformation formulas for balanced and well-poised basic hypergeometric series. To illustrate the usefulness of these formulas some examples are drawn from orthogonal polynomials.

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Authors and Affiliations

  1. Department of Mathematics & Statistics, Carlton University, Ottowa, Ontario, Canada

    Mizan Rahman

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  1. Mizan Rahman
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Editor information

Editors and Affiliations

  1. Department of Mathematics, The Ohio State University, Columbus, Ohio, USA

    Paul Nevai

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© 1990 Kluwer Academic Publishers

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Rahman, M. (1990). Some Extensions of the Beta Integral and the Hypergeometric Function. In: Nevai, P. (eds) Orthogonal Polynomials. NATO ASI Series, vol 294. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0501-6_15

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  • DOI: https://doi.org/10.1007/978-94-009-0501-6_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6711-9

  • Online ISBN: 978-94-009-0501-6

  • eBook Packages: Springer Book Archive

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