Asymptotic expansions of the Hurwitz-Lerch zeta function

60Citations
Citations of this article
12Readers
Mendeley users who have this article in their library.

Abstract

The Hurwitz-Lerch zeta function Φ(z,s,a) is considered for large and small values of a ∈ ℂ, and for large values of z ∈ ℂ, with Arg(a) < π, z ∉ [1, ∞) and s ∈ ℂ. This function is originally defined as a power series in z, convergent for z < 1, s ∈ ℂ and 1-a ∉ ℕ. An integral representation is obtained for Φ (z,s,a) which define the analytical continuation of the Hurwitz-Lerch zeta function to the cut complex z-plane ℂ\ [1, ∞). From this integral we derive three complete asymptotic expansions for either large or small a and large z. These expansions are accompanied by error bounds at any order of the approximation. Numerical experiments show that these bounds are very accurate for real values of the asymptotic variables. © 2004 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Ferreira, C., & López, J. L. (2004). Asymptotic expansions of the Hurwitz-Lerch zeta function. Journal of Mathematical Analysis and Applications, 298(1), 210–224. https://doi.org/10.1016/j.jmaa.2004.05.040

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free