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A New Family of the λ -Generalized Hurwitz-Lerch Zeta Functions with Applications |
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PP: 1485-1500 |
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Author(s) |
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H. M. Srivastava,
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Abstract |
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| Motivated largely by a number of recent investigations, we introduce and investigate the various properties of a certain new
family of the l -generalized Hurwitz-Lerch zeta functions. We derive many potentially useful results involving these l -generalized
Hurwitz-Lerch zeta functions including (for example) their partial differential equations, new series and Mellin-Barnes type contour
integral representations (which are associated with Fox’s H-function) and several other summation formulas.We discuss their potential
application in Number Theory by appropriately constructing a seemingly novel continuous analogue of Lippert’s Hurwitz measure.
We also consider some other statistical applications of the family of the l -generalized Hurwitz-Lerch zeta functions in probability
distribution theory. |
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