doi:10.1016/j.jnt.2016.08.013engFerreira, E. M.Kohara, A. K.Sesma, J.New properties of the Lerch's transcendentART-2017-96642A new representation of the Lerch''s transcendent F(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 F(z, n, a) and F(1/z, n, 1-a), which in turn provides an expansion of F(z, n, a) as a power series of 1/z, convergent for |z|>1.2017http://zaguan.unizar.es/record/7888310.1016/j.jnt.2016.08.013http://zaguan.unizar.es/record/78883oai:zaguan.unizar.es:78883info:eu-repo/grantAgreement/ES/DGA/E24-1info:eu-repo/grantAgreement/ES/MICINN/MTM2009-11154JOURNAL OF NUMBER THEORY 172 (2017), 21-31by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess