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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.
#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
#fractional derivative operator
#probability density function
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참고문헌 (28)
참고문헌 신청
A. A. Kilbas / 2006 / Theory and Applications of Fractional Differential Equations / Elsevier (North-Holland) Science Publishers
A. C¸ etinkaya / 2013 / The incomplete second Appell hypergeometric functions / Appl. Math. Comput 219 (15) : 8332 ~ 8337
A. Erd´elyi / 1953 / Higher Transcendental Functions, Vol. I / McGraw-Hill Book Company
A. M. Mathai / 2010 / The H-Functions: Theory and Appli-cations / Springer
D. Jankov / 2011 / An extended general HurwitzLerch zeta function as a Mathieu (a, γ)-series / Appl. Math. Lett 24 : 1473 ~ 1476
A. C¸ etinkaya / 2013 / The incomplete second Appell hypergeometric functions / Appl. Math. Comput 219 (15) : 8332 ~ 8337
A. Erd´elyi / 1953 / Higher Transcendental Functions, Vol. I / McGraw-Hill Book Company
A. M. Mathai / 2010 / The H-Functions: Theory and Appli-cations / Springer
D. Jankov / 2011 / An extended general HurwitzLerch zeta function as a Mathieu (a, γ)-series / Appl. Math. Lett 24 : 1473 ~ 1476
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