文摘
A new representation of the Lerch's transcendent Φ(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 bbfe9d1e81858757" title="Click to view the MathML source">Φ(z,n,a) and Φ(1/z,n,1−a), which in turn provides an expansion of bbfe9d1e81858757" title="Click to view the MathML source">Φ(z,n,a) as a power series of bbfae0dc616aca" title="Click to view the MathML source">1/z, convergent for |z|>1.