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Some new integral representations of generalized Mathieu series and alternating Mathieu series

The main purpose of this paper is to present a number of new integral representations for the familiar Mathieu series $S_\mu(r ; \{; ; a_k\}; ; _{; ; k=1}; ; ^\infty)$ defined by Srivastava and Tomovski [12]as well as for its alternating version introduced by Pog\'any et al. [8], when $a_k = k^p, (k!)^p, (\ln k!)^p$, with $p>0$.

Mathieu type series; Alternating Mathieu type series; Integral representation; Dirichlet series

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