eng Science and Education Publishing Turkish Journal of Analysis and Number Theory ISSN Pending 2013-11-01 1 1 26 35 10.12691/tjant-1-1-7 TJANT2013117 article H. M. Srivastava harimsri@math.uvic.ca 1 Min-Jie Luo 2 R. K. Raina 3 Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada Department of Applied Mathematics, Donghua University, Shanghai, People’s Republic of China Department of Mathematics, M. P. University of Agriculture and Technology, Rajasthan, India 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. http://pubs.sciepub.com/tjant/1/1/7/tjant-1-1-7.pdf 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