Certain families of series associated with the Hurwitz–Lerch zeta function. (English) Zbl 1082.11052

Choi, Junesang; Srivastava, H. M.

Appl. Math. Comput. 170, No. 1, 399-409 (2005).

Summary: The history of problems of evaluation of series associated with the Riemann zeta-function can be traced back to Christian Goldbach (1690–1764) and Leonhard Euler (1707-1783). Many different techniques to evaluate various series involving the zeta and related functions have since then been developed. The authors show how elegantly certain families of series involving the Hurwitz-Lerch zeta-function can be evaluated by starting with a single known identity for the Hurwitz-Lerch zeta-function. Some of the special cases of these series identities are also shown to lead to certain known families of summation formulas involving the Hurwitz zeta-function.

MSC:

11M35

Hurwitz and Lerch zeta functions

Keywords:

Multiple Gamma functions; Riemann Zeta function; Generalized (or Hurwitz) Zeta function; Hurwitz-Lerch Zeta function; Psi (or Digamma) function; Determinants of Laplacians; Harmonic numbers; Series identities; Summation formulas

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