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arXiv · 2510.15920

A Generalization of the Fox H-function

Jayme Vaz
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Abstract

In this paper we present a generalization of the Fox H-function called Fox-Barnes J-function. Like the Fox H-function, it is defined as a contour integral in the complex plane, but instead of an integrand given by a ratio of products of gamma functions involving several parameters, we use a ratio of products of double gamma functions. We study the conditions for its existence and how to choose a contour of integration based on the involved parameters. We discuss how the Fox H-function appears as a particular case and prove some properties of the Fox-Barnes J-function. As an application, we show how the Laplace transform of the Kilbas-Saigo function can be conveniently written in terms of the Fox-Barnes J-function, even in cases where the usual series representation is not convergent.

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Jayme Vaz. 2025-10-01. A Generalization of the Fox H-function. https://arxiv.org/abs/2510.15920

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