Summation of Series over Bourget Functions

Canadian mathematical bulletin

关键词: Riemann zeta function;    Bessel functions;    Bourget functions;    Dirichlet functions;   

DOI  :  10.4153/CMB-2008-062-6

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper we derive formulas for summation of series involvingJ.~Bourget's generalization of Bessel functions of integer order, aswell as the analogous generalizations by H.~M.~Srivastava. These series areexpressed in terms of the Riemann $z$ function and Dirichletfunctions $eta$, $la$, $$, and can be brought into closed form incertain cases, which means that the infinite series are representedby finite sums.

【 授权许可】

Unknown