On the \(H\)-function (Q1307625)

The authors study the well known Fox's H-function. By considering the asymptotic behaviour of the gamma functions which define the H-function as a Mellin Barnes type integral at infinity, and following earlier work of \textit{B. L. J. Braaksma} [Compos. Math. 15, 239-341 (1964; Zbl 0129.28604)], the conditions of existence and series representation (and power-logarithmic series expansion) of the H-function are obtained. The paper describes the already known results on the H-function under more precise conditions.