Remark on the Hurwitz-Lerch zeta function

Fixexd point theory and applications

Junesang Choi¹ 

[1] Department of Mathematics, Dongguk University, Gyeongju, Korea

关键词: gamma function;    Riemann zeta function;    generalized (or Hurwitz) zeta function;    Poisson summation formula;    Lerch zeta function;    Hurwitz-Lerch zeta function;   

DOI  :  10.1186/1687-1812-2013-70

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Various generalizations of the Hurwitz-Lerch zeta function have been actively investigated by many authors. Very recently, Srivastava presented a systematic investigation of numerous interesting properties of some families of generating functions and their partial sums which are associated with various classes of the extended Hurwitz-Lerch zeta functions. In this paper, firstly, we show that by using the Poisson summation formula, the analytic continuation of the Lerch zeta function can be explained and the functional relation for the Lerch zeta function can be obtained in a very elementary way. Secondly, we present another functional relation for the Lerch zeta function and derive the well-known functional relation for the Hurwitz zeta function from our formula by following the lines of Apostol’s argument. MSC: 11M99, 33B15, 42A24, 11M35, 11M36, 11M41, 42A16.

【 授权许可】

CC BY