engleski

Generalization of the Quotient Mean Series

In this paper a new family of generalized Mathieu series, called Quotient mean Matheu series is introduced. Namely, some generalized Mathieu series, like Mathieu (alpha, lambda)- series, Mathieu a-series and their alternating variants are represented in terms of Quotient mean Mathieu series. By using the Laplace integral formulas and Euler-MacLaurin summation formula for Dirichlet series, some new integral representations are given.

Quotient mean Mathieu series ; Dirichlet-series ; Mathieu series ; means ; gamma function ; Euler-Maclaurin summation formula

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