New properties of the Lerch's transcendent

Abstract

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 provides an expansion of Phi(z,n,a) as a power series of 1/z, convergent for |z|>1.

arXiv comment11 pages, 1 figure

References in corpus (4)

• Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent
• Representation of Integral Dispersion Relations by Local Forms
• The Lerch zeta function III. Polylogarithms and special values
• Two-point derivative dispersion relations

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