New properties of the Lerch's transcendent

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• 作者：E.M. Ferreira^a ; ^{erasmo@if.ufrj.br" class="auth_mail" title="E-mail the corresponding author} ; A.K. Kohara^a ; ^{kendi@if.ufrj.br" class="auth_mail" title="E-mail the corresponding author} ; J. Sesma^b ; ^{javier@unizar.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11M35 ; 30E15
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：172
• 期：Complete
• 页码：21-31
• 全文大小：290 K

文摘

A new representation of the Lerch's transcendent Φ(z,s,a)$\mathrm{\Phi }(z,s,a)$, valid for positive integer s=n=1,2,…$s=n=1,2,\dots$ and for z and a   belonging to certain regions of the complex plane, is presented. It allows to write an equation relating Φ(z,n,a)$\mathrm{\Phi }(z,n,a)$ and Φ(1/z,n,1−a)$\mathrm{\Phi }(1/z,n,1-a)$, which in turn provides an expansion of Φ(z,n,a)$\mathrm{\Phi }(z,n,a)$ as a power series of 1/z$1/z$, convergent for |z|>1$|z|>1$.