Some Useful Collective Properties of Bessel, Marcum Q-Functions and Laguerre Polynomials

TL;DR

This paper derives new properties and interrelations among Bessel functions, Marcum Q-functions, and Laguerre polynomials to aid in solving complex problems involving special functions in applied sciences.

Contribution

It introduces novel properties and relationships among these special functions, facilitating solutions to previously intractable problems.

Findings

Derived new properties of Bessel functions

Established interrelations between Marcum Q-functions and Laguerre polynomials

Provided tools for solving complex integrals involving special functions

Abstract

Special functions have been used widely in many problems of applied sciences. However, there are considerable numbers of problems in which exact solutions could not be achieved because of undefined sums or integrals involving special functions. These handicaps force researchers to seek new properties of special functions. Many problems that could not be solved so far would be solved by means of these efforts. Therefore in this article, we derived some useful properties and interrelations of each others of Bessel functions, Marcum Q-functions and Laguerre polynomials.