engleski

On multiple Mathieu $(a, \lambda)$-series

In this paper we introduce the multiple Mathieu $(a, \lambda)$-series. We obtain two integral representations for multiple Mathieu $(a, \lambda)$-series applying Ivanov-s and Poga\'any's variant of the multiple Euler-Maclaurin summation formula. Then, a bilateral bounding inequality is derived by virtue of the achieved integral expressions. Finally, the special case of mutiple Mathieu $a$-series has been investigated.

Mathieu type series ; Multiple Mathieu type series ; Multiple Mathieu $(a ; \lambda)$-series ; Dirichlet series ; r-dimensional Euler-Maclaurin summation formula

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