An extension of a series containing Laguerre polynomials

A K Rathie; R B Paris

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arXiv · 1411.5257

An extension of a series containing Laguerre polynomials

A K Rathie·R B Paris

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Abstract

Expressions for the summation of the series involving the Laguerre polynomials \[S_m(\pmν, \pm p)\equiv e^{-x}\sum_{n=0}^\infty \frac{x^n\,L_n^{(ν)}(x)}{(1\pm ν\pm p)_n}\frac{(f+m)_n}{(f)_n}\] for any non-negative integers $m$ and $p$ are obtained in terms of generalized hypergeometric functions. These results extend previous work in the literature.

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A K Rathie, R B Paris. 2014-11-19. An extension of a series containing Laguerre polynomials. https://arxiv.org/abs/1411.5257

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