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## Homework Statement

consider the integral,

[tex]{C_\ell } = \frac{{2\ell + 1}}{{2{j_\ell }(kr)}}\frac{1}{{{2^\ell }\ell !}}\int_{ - 1}^{ + 1} {\frac{{{d^\ell }({{({x^2} - 1)}^\ell })}}{{d{x^\ell }}}{e^{{\bf{i}}krx}}dx} [/tex]

how do you do it?

## Homework Equations

l = integer, as in the oft-occurring l*(l+1)*hbar

j sub l = the l-th bessel function

x = cos(theta)

## The Attempt at a Solution

this is related to Shankar 12.6.10