I have given a function $$a(m,n,\mu,\nu,p):=\frac{2p+1}{2}\frac{(p-m-\mu)!}{(p+m+\mu)!}\int_{-1}^1 P^m_n(x)P^\mu_{\nu}(x)P^{m+\mu}_p(x)dx.$$ (of course all parameters are appropriate integers, so that everything behaves well). The $P^m_n$ are associated Legendre polynomials. The thing is that I want to compute this function in Matlab and I do not want to have an integral in there, hence I am looking for a nice solution of this.
If you do not have an idea how to solve it, but think that you know a way how to deal with this numerically better than solving numerically this integral, your answer is also HIGHLY APPRECIATED!
This might be helpful, no? Google is your friend!
http://en.wikipedia.org/wiki/Associated_Legendre_polynomials#Gaunt.27s_formula