Integral expressions are given for some families of Mathieu-type
a-series
and alternating
a-series in the case when the series terms contain: (i) the generalized hypergeometric functions
an class="inlMMLBox">an>
and (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 recently by the authors
and H.M. Srivastava.