New properties of the Lerch's transcendent

JOURNAL OF NUMBER THEORY

卷:172

Article

Ferreira, E. M.¹  Kohara, A. K.¹  Sesma, J.² 

[1] Univ Fed Rio de Janeiro, Inst Fis, BR-21941972 Rio De Janeiro, Brazil

[2] Fac Ciencias, Dept Fis Teor, Zaragoza 50009, Spain

关键词: Lerch's transcendent;    Hurwitz zeta function;    Polylogarithms;   

DOI  :  10.1016/j.jnt.2016.08.013

来源: Elsevier

【 摘 要 】

A new representation of the Lerch's transcendent Phi(z, s, a), valid for positive integer s = n = 1,2, ... and for z and a belonging to certain regions of the complex plane, is presented. It allows to write an equation relating Phi(z, n, a) and. Phi(1/z,n, 1 - a), which in turn provides an expansion of Phi(z, n, a) as a power series of 1/z, convergent for vertical bar z vertical bar > 1. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free