engleski

On Mathieu--type series whose terms contain generalized hypergeometric function $_pF_q$ and Meijer's $G$--function

Integral expressions are given for some families of Mathieu-type \textbf a-series and alternating \textbf a-series in the case, when the series terms contain \textbf{; ; ; ; (i)}; ; ; ; generalized hypergeometric functions ${; ; ; }; ; ; _pF_q$ and \textbf{; ; ; (ii)}; ; ; ; Meijer's $G$-function. Using the derived integral representations, bounding inequalities are obtained for these series. The derived integral expressions and the consequent two-sided bounding inequalities generalize some known results published nowadays by the authors and H. M. Srivastava.

Mathieu $\mathbf a$--; and alternating Mathieu $\mathbf a$--series; Dirichlet series; generalized hypergeometric function $_pF_q $; Meijer's $G$--function; Laplace integral; integral representations; incomplete Gamma--function; exponenetial bounds

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