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Journal Article

Reducibility of Certain Kampé De Fériet Function with an Application to Generating relations for products of two Laguerre polynomials

Junesang Choi and Arjun K. Rathie
Filomat
Vol. 30, No. 7, The 22nd International Conference on Finite and Infinite Dimensional Complex Analysis and Applications (2016), pp. 2059-2066
Stable URL: http://www.jstor.org/stable/24898776
Page Count: 8

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Topics: Mathematical functions, Hypergeometric functions, Polynomials
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Reducibility of Certain Kampé De Fériet Function with an Application to Generating relations for products of two Laguerre polynomials
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Abstract

Abstract. It has been an interesting and natural research subject to consider the reducibility of some extensively generalized special functions. In this regard, Kampé de Fériet function has been attracted by many mathematicians. The authors [7] also established many interesting cases of the reducibility of Kampé de Fériet function by employing generalizations of the two results for the terminating ₂𝐹₁(2) hypergeometric identities due to Kim et al. In this sequel, we first aim at presenting several interesting cases of the reducibility of Kampé de Fériet function by using generalizations of classical Kummer's summation theorem due to Lavoie et al. We next show how one can use the above-given result to obtain eleven new generating relations for products of two Laguerre polynomials in a single-form result. We also consider many interesting and potentially useful specials cases of our main results.

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