Some Mathieu-type series for generalized H-function associated with a certain class of Feynman integrals

Abstract

Closed form expressions are investigated for a family of convergent Mathieu type a-series and its alternating variant, whose terms contain a generalized H-function associated with certain Feynman integrals. The results derived are of general character and provide an elegant generalization for the closed form expressions of these series associated with the H-function by Pogány [Integral expressions of Mathieu-type series whose terms contain Fox's H-function, Appl. Math. Lett. 20 (2007), pp. 764–769], for Fox–Wright Ψ-functions by Pogány and Srivastava [Some Mathieu-type series associated with the Fox–Wright function, Comput. Math. Appl. 57 (1) (2009), pp. 127–140] and for p F q and Meijer's G-function by Pogány and Tomovski [On Mathieu-type series which terms contain generalized hypergeometric function p F q and Meijer's G-function, Math. Comput. Modell. 47 (9–10) (2008), pp. 952–969], and others.