On a new class of summation formulae involving the Laguerre polynomial

Yong S. Kim, Arjun K. Rathie, Richard B. Paris

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Abstract

By elementary manipulation of series, a general transformation involving the generalized hypergeometric function is established. Kummer’s first theorem, the classical Gauss summation theorem and the generalized Kummer summation theorem due to Lavoie et al. [Generalizations of Whipple’s theorem on the sum of a 3 F 2, J. Comput. Appl. Math. 72 (1996), pp. 293–300] are then applied to obtain a new class of summation formulae involving the Laguerre polynomial, which have not previously appeared in the literature. Several related results due to Exton have also been given in a corrected form.
Original languageEnglish
Pages (from-to) 435-444
Number of pages10
JournalIntegral Transforms and Special Functions
Volume23
Issue number6
DOIs
Publication statusPublished - 2012

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