New Integral Representations for the Bessel Functions

TL;DR

This paper introduces new integral formulas for Bessel functions and uses them to derive an expression for the Modified Bessel K function, enhancing analytical tools for these special functions.

Contribution

The paper presents novel integral representations for Bessel J and I functions, and derives a new expression for the Modified Bessel K function.

Findings

New integral representations for Bessel J and I functions.

Derived an expression for the Modified Bessel K function.

Enhanced analytical methods for Bessel functions.

Abstract

In this paper, new integral representations for the Bessel $J$ and $I$ functions were presented and their results were used to derive an expression for the Modified Bessel $K$ function.