# Integration of a product of legendre polynomials in matlab

1. Aug 19, 2011

### vanmil

I am trying to find a way to integrate the following expression
Integral {Ylm(theta, phi) Conjugate (Yl'm'(theta, phi) LegendrePolynomial(n, Cos[theta])} dtheta dphi

for definite values of l,m,n,l',m' . You normally do this in Mathematica very easily. But it happens that I need to use this integral in Matlab for many different values of l,m,n,l',m' as it will be part of of more code in a program I am writing. Is there any efficient way to solve this integral? I was thinking to convert the spherical harmonics terms into associated legendre polynomials following the formula to do this and then multiply by the other legendre polynomial (third term in the expression above). I am new to Matlab therefore I am not sure what approach to follow. Would it be easier doing this in other language or software.. except Mathematica!

Thanks and hope you can help

2. Aug 19, 2011

### Pythagorean

for future reference, numerical integration technique is often called "quadrature":

http://www.mathworks.com/help/techdoc/math/bsgprfe-1.html [Broken]

Last edited by a moderator: May 5, 2017