The generalized Marcum $Q-$function: an orthogonal polynomial approach

TL;DR

This paper introduces a new power series representation for the generalized Marcum Q-function using generalized Laguerre polynomials, demonstrating its convergence and providing numerical validation.

Contribution

It presents a novel orthogonal polynomial-based power series expansion for the generalized Marcum Q-function, with convergence analysis and numerical results.

Findings

Power series converges absolutely

Fast convergence demonstrated through error analysis

Numerical results validate the theoretical expansion

Abstract

A novel power series representation of the generalized Marcum $Q-$function of positive order involving generalized Laguerre polynomials is presented. The absolute convergence of the proposed power series expansion is showed, together with a convergence speed analysis by means of truncation error. A brief review of related studies and some numerical results are also provided.