New properties of the Lerch's transcendent
Number Theory
2016-10-26 v2 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.1601.02094,
title = {New properties of the Lerch's transcendent},
author = {E. M. Ferreira and A. K. Kohara and J. Sesma},
journal= {arXiv preprint arXiv:1601.02094},
year = {2016}
}
Comments
11 pages, 1 figure