An Analytical Evaluation For The Integral Of Two Spherical Bessel Functions With An Additional Exponential And Polynomial Factor

Details An Analytical Evaluation For The Integral Of Two Spherical Bessel Functions With An Additional Exponential And Polynomial Factor An Analytical Evaluation For The Integral Of Two Spherical Bessel Functions With An Additional Exponential And Polynomial Factor

2011-10-27

arxiv.org/abs/1110.6147v1

Physics

Mathematical Physics

7 Pages

Scientific paper

The integrals $\threej{\Llo}{\Llt}{\Llth} {0}{0}{0}\,\int_0^\infty
\,r^{\Llth+1}\,e^{-\alpha r}\,j_\Llo(k_1r)\, j_\Llt(k_2r)\,dr$ and
$\threej{\Llo}{\Llt}{\Llth} {0}{0}{0}\,\int_0^\infty \,r^{\Llth+2}\,e^{-\alpha
r}\,j_\Llo(k_1r)\, j_\Llt(k_2r)\,dr$ are evaluated analytically. The result is
a finite sum over the associated Legendre function of the second kind.

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