Numerical analysis for the moments of Bessel functions and Bessel-trigonometric functions

TL;DR

This paper provides a comprehensive analysis of the moments of Bessel and Bessel-trigonometric functions, introducing efficient numerical schemes and closed-form expressions validated through numerical experiments.

Contribution

It offers a complete recursive analysis and a fast numerical scheme for moments of Bessel functions, along with closed-form solutions for Bessel-trigonometric functions.

Findings

Proposed a fast numerical scheme for Bessel function moments.

Derived closed-form expressions for Bessel-trigonometric function moments.

Validated the accuracy and efficiency through numerical experiments.

Abstract

The moments of Bessel functions and Bessel-trigonometric functions play a basic role in many practical problems and numerical analysis. This paper presents a complete analysis for these moments based on the recursive relations of Bessel functions. To evaluate the moments of Bessel functions numerically, a fast and efficient scheme is also proposed to approximate the integral of Bessel function of the first kind and of zero order. The moments of Bessel-trigonometric functions are proved to be expressed in a closed form. In the numerical results, the accuracy and efficiency of the proposed analysis for the moments of Bessel functions is validated first and then by comparing the existing methods, a better scheme for the moments of Bessel functions is presented.