# A new Weber type integral equation related to the Weber-Titchmarsh problem

## TL;DR

This paper introduces a new solvability condition and closed-form solution for a Weber type integral equation, expanding understanding of Weber-Orr transforms and related classical problems using Mellin transform techniques.

## Contribution

The paper presents a novel solution method for Weber type integral equations, connecting classical Weber-Titchmarsh problems with modern Mellin transform techniques.

## Key findings

- Derived solvability conditions for the Weber type integral equation
- Obtained closed-form solutions using Mellin transform properties
- Connected classical Weber-Titchmarsh problem with modern integral transform methods

## Abstract

We derive solvability conditions and closed-form solution for the Weber type integral equation, related to the familiar Weber-Orr integral transforms and the old Weber-Titchmarsh problem (posed in Proc. Lond. Math. Soc. 22 (2) (1924), pp.15, 16), recently solved by the author. Our method involves properties of the inverse Mellin transform of integrable functions. The Mellin-Parseval equality and some integrals, involving the Gauss hypergeometric function are used.