One way to prove this is to start with the spherical harmonic expansion of a plane wave. Alternatively, you could verify directly that satifies the approproaite d.e. with initial conditions.
Can anyone help me to solve integral of function exp(i alfa x)P_n(x)dx
in limits form -1 to 1
where P_n(x) is legendre polynomial.
Solution sholud be
sqr(2pi/alfa)iJ_n+1/2(alfa)
where J_n+1/2(alfa)
is modifided bessel function
pls help!
and sorry that i written it like this but i forgot how to use latex
i couldn't attach pdf file, but i downloadeld it from this page.. Copson E.T. Introduction to the theory of functions of a complex variable (OUP, 1955)(ISBN 0198531451)(T)(455s)_MCc_.djvu - 4shared.com - online file sharing and storage - download
if it can help you
OK, I have his book and I located the question. It seems he wants to deduce Bauer's formula from the result and so we can't start with the plane wave expansion. Give me a little time to think of the argument intended by the author.