1. CMB 2008 (vol 51 pp. 627)
|Summation of Series over Bourget Functions |
In this paper we derive formulas for summation of series involving J.~Bourget's generalization of Bessel functions of integer order, as well as the analogous generalizations by H.~M.~Srivastava. These series are expressed in terms of the Riemann $\z$ function and Dirichlet functions $\eta$, $\la$, $\b$, and can be brought into closed form in certain cases, which means that the infinite series are represented by finite sums.
Keywords:Riemann zeta function, Bessel functions, Bourget functions, Dirichlet functions
Categories:33C10, 11M06, 65B10