In this paper, we study a certain class of generalized Hurwitz-Lerch zeta functions. We derive several new and useful properties of these generalized Hurwitz-Lerch zeta functions such as (for example) their partial differential equations, new series and Mellin-Barnes type contour integral representations involving Fox’s H-function and a pair of summation formulas. More importantly, by considering their application in Number Theory, we construct a new continuous analogue of Lippert’s Hurwitz measure. Some statistical applications are also given.
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Author Name: H. M. Srivastava, Min-Jie Luo, R. K. Raina
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Keywords: Hurwitz-Lerch zeta function, arithmetic density of number theory, partial differential equations, series and Mellin-Barnes type contour integral representations, Fox’s H-function, summation formulas, generalized Hurwitz meausure, probability density function, moment generating function
ISSN: 2333-1100
EISSN: 2333-1232
EOI/DOI: 10.12691/tjant-1-1-7
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