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Incomplete extended Hurwitz-Lerch zeta functions and associated properties

Rakesh K. Parmar|Ram K. Saxena
대한수학회 (The Korean Mathematical Society)|2017.04|대한수학회논문집 (Communications of the KMS)|제32권 제2호|pp. 287-304

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키워드

probability density functionPochhammer symbolgamma functionsincomplete gamma functionsincomplete Pochhammer symbolsincomplete generalized hypergeometric functionsincomplete Fox-Wright functiongeneralized Hurwitz-Lerch zeta functionincomplete Hurwitz-Lerch zeta functionfractional derivative operator
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초록

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [\emph{Integral Transforms Spec. Funct.} 23 (2012), 659--683] by means of the incomplete Pochhammer symbols $ \left(\lambda; \kappa\right)_{\nu} $ and $ \left[\lambda; \kappa \right]_{\nu}$, we first introduce incomplete Fox-Wright function. We then define the families of incomplete extended Hurwitz-Lerch Zeta function. We then systematically investigate several interesting properties of these incomplete extended Hurwitz-Lerch Zeta function which include various integral representations, summation formula, fractional derivative formula. We also consider an application to probability distributions and some special cases of our main results.

Abstract

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [\emph{Integral Transforms Spec. Funct.} 23 (2012), 659--683] by means of the incomplete Pochhammer symbols $ \left(\lambda; \kappa\right)_{\nu} $ and $ \left[\lambda; \kappa \right]_{\nu}$, we first introduce incomplete Fox-Wright function. We then define the families of incomplete extended Hurwitz-Lerch Zeta function. We then systematically investigate several interesting properties of these incomplete extended Hurwitz-Lerch Zeta function which include various integral representations, summation formula, fractional derivative formula. We also consider an application to probability distributions and some special cases of our main results.

참고문헌 (34)

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관련 논문AI추천

Extension of Generalized Hurwitz-Lerch Zeta Function and Associated Properties최준상, Rakesh Kumar Parmar, Ravinder Krishna Raina경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2017 · 제57권 제3호An extension of the extended Hurwitz-Lerch Zeta Functions of Two Variables최준상, Rakesh K. Parmar, Ram K. Saxena대한수학회 · 대한수학회보2017 · 제54권 제6호On Extended Hurwitz-Lerch Zeta FunctionMaged Gumman Bin-Saad, Mohammed Ahmed Pathan, Mohannad Jamal Said Shahwan경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2023 · 제63권 제3호The Incomplete Lauricella Functions of Several Variables and Associated Properties and Formulas최준상, H. M. Srivastava, Rakesh K. Parmar경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2018 · 제58권 제1호The incomplete generalized $\tau$-hypergeometric and second $\tau$-Appell functionsRakesh Kumar Parmar, Ram Kishore Saxena대한수학회 · 대한수학회지2016 · 제53권 제2호A FURTHER GENERALIZATION OF EXTENDED HURWITZ-LERCH ZETA FUNCTION OF TWO VARIABLESPRAKRITI RAI, SANIYA BATRA장전수학회 · Advanced Studies in Contemporary Mathematics2020 · 제30권 제3호

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