Some Mathieu-type series associated with the Fox–Wright function

Closed-form integral expressions are derived here for a family of convergent Mathieu-type series and its alternating variant when their terms contain the Fox–Wright pΨqpΨq function. Some two-sided exponential bounding inequalities are then obtained for a class of Fox–Wright pΨqpΨq functions, thereby generalizing certain results of Luke. Finally, by means of the integral expressions obtained here, a number of two-sided exponential bounding inequalities are given for the aforementioned series.