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.
Digital Object Identifier (DOI)
M. Srivastava, H.
"A New Family of the λ -Generalized Hurwitz-Lerch Zeta Functions with Applications,"
Applied Mathematics & Information Sciences: Vol. 08
, Article 2.
Available at: https://dc.naturalspublishing.com/amis/vol08/iss4/2