A remarkable double integral of the product of two Gaussian hypergeometric functions

2023/02/27 by Diekema, E.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.13901

Abstract

In this paper a double integral containing two Gaussian hypergeometric functions is discussed. The integral is not found in the literature and a direct computation is not (yet) possible. Therefore, a complete different integral is computed by two methods. The first method gives a combination of hypergeometric functions and the requested original integral, while with the second method this different integral can be computed directly. Equalization of the results from both methods gives the requested integral.

Related

• Non-Gaussian integrals and general hypergeometric functions
• A New Class of Integrals Involving Extended Hypergeometric Function
• On a new result for the hypergeometric function
• On the dual valued generalized hypergeometric function and its special cases
• Γ-evaluations of hypergeometric series