A generalization for the infinite integral over three spherical Bessel functions

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