Commun. Korean Math. Soc. 2017; 32(2): 287-304
Online first article April 17, 2017 Printed April 30, 2017
https://doi.org/10.4134/CKMS.c150227
Copyright © The Korean Mathematical Society.
Rakesh K. Parmar and Ram K. Saxena
Government College of Engineering and Technology, Jai Narain Vyas University
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.
Keywords: gamma functions, incomplete gamma functions, Pochhammer symbol, incomplete Pochhammer symbols, incomplete generalized hypergeometric functions, incomplete Fox-Wright function, generalized Hurwitz-Lerch zeta function, incomplete Hurwitz-Lerch zeta function
MSC numbers: Primary 11M06, 11M35, 33B15, 33C60; Secondary 11B68, 33C65, 33C90
2018; 33(1): 127-142
2015; 30(4): 439-446
2015; 30(2): 103-108
2013; 28(3): 527-534
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