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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Generating functions for Jacobi and related polynomials


Author: I. A. Khan
Journal: Proc. Amer. Math. Soc. 32 (1972), 179-186
MSC: Primary 33A65
MathSciNet review: 0348161
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Abstract: In the present paper, we have established the following relation involving Kampe de Feriet's double hypergeometric function of superior order

$\displaystyle F\left[ {\begin{array}{*{20}{c}} p \\ 1 \\ q \\ 0 \\ \end{array} ... ...n{array}{*{20}{c}} { - n,b;} \\ {1 + b' - n;} \\ \end{array} x} \right]{y^n},} $

which yields a number of interesting generating formulae for Jacobi and related polynomials.

A large number of special cases have been also discussed.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0348161-X
Article copyright: © Copyright 1972 American Mathematical Society