On the generalized Dixon integral equation

TL;DR

This paper derives a unique analytic solution for the generalized Dixon integral equation using Neumann series and residue calculus, advancing the mathematical understanding of such integral equations.

Contribution

It provides the first explicit solution in terms of Neumann series for the generalized Dixon integral equation, including residue analysis at multiple poles.

Findings

Explicit solution expressed as a double series of residues

Solution valid in the space of continuously differentiable functions on [0,A]

Advances analytical methods for solving generalized integral equations

Abstract

A unique analytic solution of the generalized Dixon nonhomogeneous integral equation is derived in $C^{1}[0,A],\ A > 0$. It is written in terms of the Neumann series, which is expressed as a double series of residues at multiple poles of powers of the gamma-function.