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The Incomplete Lauricella Functions of Several Variables and Associated Properties and Formulas

H. M. Srivastava|최준상|Rakesh K. Parmar
경북대학교 자연과학대학 수학과|2018.03|Kyungpook Mathematical Journal|제58권 제1호|pp. 19-35|DOI https://doi.org/10.5666/KMJ.2018.58.1.19

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키워드

Gamma functionsLaguerre polynomialsPochhammer symbolAppell functionsincomplete gamma functionsincomplete Pochhammer symbolsincomplete generalized hypergeometric functionsLauricella functionsBessel and modi ed Bessel functionsincomplete second Appell functionsMarcum q- and Q-functions
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초록

Motivated mainly by certain interesting recent extensions of the generalizedhypergeometric function [30] and the second Appell function [6], we introduce here theincomplete Lauricella functions $\gamma_{A}^{(n)}$ and $\Gamma_{A}^{(n)}$ of n variables. We then systematically investigateseveral properties of each of these incomplete Lauricella functions including, forexample, their various integral representations, nite summation formulas, transformationand derivative formulas, and so on. We provide relevant connections of some of the specialcases of the main results presented here with known identities. Several potential areas ofapplication of the incomplete hypergeometric functions in one and more variables are alsopointed out.

Abstract

Motivated mainly by certain interesting recent extensions of the generalizedhypergeometric function [30] and the second Appell function [6], we introduce here theincomplete Lauricella functions $\gamma_{A}^{(n)}$ and $\Gamma_{A}^{(n)}$ of n variables. We then systematically investigateseveral properties of each of these incomplete Lauricella functions including, forexample, their various integral representations, nite summation formulas, transformationand derivative formulas, and so on. We provide relevant connections of some of the specialcases of the main results presented here with known identities. Several potential areas ofapplication of the incomplete hypergeometric functions in one and more variables are alsopointed out.

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관련 논문AI추천

Extended Lauricella and Appell Functions and Their Associated PropertiesH. M. Srivastava, M. M. Joshi, R. K. Parmar장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제2호EXTENSIONS OF MULTIPLE LAURICELLA AND HUMBERT’S CONFLUENT HYPERGEOMETRIC FUNCTIONS THROUGH A HIGHLY GENERALIZED POCHHAMMER SYMBOL AND THEIR RELATED PROPERTIES최준상, Naveen Kumar, Rakesh K. Parmar, RITU AGARWAL대한수학회 · 대한수학회보2023 · 제60권 제3호The incomplete generalized $\tau$-hypergeometric and second $\tau$-Appell functionsRakesh Kumar Parmar, Ram Kishore Saxena대한수학회 · 대한수학회지2016 · 제53권 제2호Some $\tau$-extensions of Lauricella functions of several variablesRakesh Kumar Parmar, Shyam Lal Kalla, Sunil Dutt Purohit대한수학회 · 대한수학회논문집2015 · 제30권 제3호Generalized Incomplete Pochhammer Symbols and Their Applications to Hypergeometric functionsAshish Verma, Vivek Sahai경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2018 · 제58권 제1호Extended hypergeometric functions of two and three variables최준상, Praveen Agarwal, Shilpi Jain대한수학회 · 대한수학회논문집2015 · 제30권 제4호

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