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Extended Lauricella and Appell Functions and Their Associated Properties

H. M. Srivastava|R. K. Parmar|M. M. Joshi
장전수학회 (Jangjeon Mathematical Society)|2015.04|Advanced Studies in Contemporary Mathematics|제25권 제2호|pp. 151-165

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참고문헌

키워드

Laguerre polynomialsAppell functionsExtended gamma functionsGeneralized Pochhammer symbolGeneralized Gauss hypergeometric functionLauricella functionsIncomplete gamma functionsBessel and modi- ed Bessel functionsExtended second Appell function in two variablesExtended Lauricella functions of several variables
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초록

Recently, an extension of the Pochhammer symbol was used in order to introduce and investigate a family of generalized hypergeometric functions (see [20]). The main object of this paper is to present an extension of the Lauricella function F(n) A of n variables and investi- gate its several properties including, for example, its various integral representations, transformation formulas, derivative formulas and re- currence relations. In particular, for n = 2, we get the corresponding extension of the second Appell hypergeometric function F2 and de- duce its above-mentioned properties. Relevant connections of the main results presented in this paper with various (known or new) results are also pointed out.

Abstract

Recently, an extension of the Pochhammer symbol was used in order to introduce and investigate a family of generalized hypergeometric functions (see [20]). The main object of this paper is to present an extension of the Lauricella function F(n) A of n variables and investi- gate its several properties including, for example, its various integral representations, transformation formulas, derivative formulas and re- currence relations. In particular, for n = 2, we get the corresponding extension of the second Appell hypergeometric function F2 and de- duce its above-mentioned properties. Relevant connections of the main results presented in this paper with various (known or new) results are also pointed out.

참고문헌 (30)

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