Transformation formulas for multivariable basic hypergeometric series
نویسندگان
چکیده
منابع مشابه
Transformation formulas for multivariable basic hypergeometric series
Abstract. We study multivariable (bilateral) basic hypergeometric series associated with (type A) Macdonald polynomials. We derive several transformation and summation properties for such series, including analogues of Heine’s 2φ1 transformation, the q-Pfaff-Kummer and Euler transformations, the q-Saalschütz summation formula, and Sear’s transformation for terminating, balanced 4φ3 series. For ...
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Abstract. We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent multivariable extensions of the terminating very-well-poised 6φ5 summation formula. We derive several new related identities including ...
متن کامل0 M ar 1 99 8 Transformation formulae for multivariable basic hypergeometric series
We study multivariable (bilateral) basic hypergeometric series associated with (type A) Macdonald polynomials. We derive several transformation and summation properties for such series including analogues of Heine's 2 φ 1 transformation, the q-Pfaff-Kummer and Euler transformations, the q-Saalschütz summation formula and Sear's transformation for terminating, balanced 4 φ 3 series. For bilatera...
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Abstract. We present relatively simple and direct proofs of the integral representations established recently in [7]. An algorithm is then furnished and applied to obtain new classes of integral formulas for the multivariable hypergeometric functions, thereby, providing generalizations to the results of [7]. Also, an operational formula involving fractional calculus operators for an analytic fu...
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ژورنال
عنوان ژورنال: Methods and Applications of Analysis
سال: 1999
ISSN: 1073-2772,1945-0001
DOI: 10.4310/maa.1999.v6.n2.a2