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A q-Extension of Feldheim's Bilinear Sum for Jacobi Polynomials and Some Applications

Published online by Cambridge University Press:  20 November 2018

Mizan Rahman
Mizan Rahman*
Affiliation:
Carleton University, Ottawa, Ontario
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The main objective of this paper is to find useful q-extensions of Feldheim's [6] bilinear formula for Jacobi polynomials, namely,

1.1

where the Appel function F4 is defined by

1.2

α1, α2, ρ are arbitrary complex parameters such that the series on both sides of (1.1) are convergent, and

1.3

is the Jacobi polynomial of degree k, (a)k being the usual shifted factorial.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 3 , 01 June 1985 , pp. 551 - 576
Copyright
Copyright © Canadian Mathematical Society 1985

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