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# Summation of Series over Bourget Functions

Published:2008-12-01
Printed: Dec 2008
• Mirjana V. Vidanovi\'{c}
• Slobodan B. Tri\v{c}kovi\'{c}
• Miomir S. Stankovi\'{c}
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## 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

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