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Summation of Series over Bourget Functions |
Published:2008-12-01
Printed: Dec 2008
Printed: Dec 2008
- Mirjana V. Vidanovi\'{c}
- Slobodan B. Tri\v{c}kovi\'{c}
- Miomir S. Stankovi\'{c}
Abstract
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 |
| MSC Classifications: |
33C10 - Bessel and Airy functions, cylinder functions, ${}_0F_1$ 11M06 - $\zeta (s)$ and $L(s, \chi)$ 65B10 - Summation of series |