Integral expressions for Mathieu-type series whose terms contain Fox’s HH-function

Closed integral form expressions are derived for the Mathieu-type a-series and for the associated alternating series whose terms contain Fox’s HH-function. In the final section, two similar results on Mathieu-type series with the Fox–Wright Psi-function Ψqp and the generalized hypergeometric function Fqp which can be expressed in terms of Fox’s HH-functions are deduced respectively.