A Generalisation For The Infinite Integral Over Three Spherical Bessel Functions

Details A Generalisation For The Infinite Integral Over Three Spherical Bessel Functions A Generalisation For The Infinite Integral Over Three Spherical Bessel Functions

2010-06-10

arxiv.org/abs/1006.2108v4

J.Phys.A43:455204,2010

Physics

Mathematical Physics

Published in J. Phys. A: Math. Theor. 43 (2010) 455204

Scientific paper

10.1088/1751-8113/43/45/455204

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

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