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 language | English |
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Pages (from-to) | 435-444 |
Number of pages | 10 |
Journal | Integral Transforms and Special Functions |
Volume | 23 |
Issue number | 6 |
Early online date | 18 Jul 2011 |
DOIs | |
Publication status | Published - 2012 |
Keywords
- Generalized hypergeometric series
- Generalized Kummer summation theorem
- Laguerre polynomials