A Generalisation For The Infinite Integral Over Three Spherical Bessel Functions

Abstract

A new formula is derived that generalises an earlier result for the infinite integral over three spherical Bessel functions. The analytical result involves a finite sum over associated Legendre functions, $P_l^m(x)$, of degree $l$ and order $m$. The sum allows for values of $|m|$ that are greater than $l$. A generalisation for the associated Legendre functions to allow for any rational $m$ for a specific $l$ is also shown