How to compute an associated legendre function given by P(n,a*m/b,x)?

Hello:

I am trying to compute an associated legendre function P(n,a*m/b,x) where n is the degree and m is the order. The inbuilt routine in MATLAB 'legendre.m' allows to enter a given n and generates the value of the polynomial for a given x where { -1 <= x <= 1 ; 0 < m < n}. However if I have an associated legendre function of the form P(n,a*m/b,x) how does one include the effect due to the constants a and b?

Please note that m continues to remain an integer in the current form. However 'a*m/b' may or may not be an integer strictly depending on the values of a and b.

Thank you.

Regards, D. Sarkar

Answer 1

[Roger Stafford]

For a non-integer value of the order, I believe the Legendre function can be evaluated using matlab's 'gamma' and 'hypergeom' functions. See the Wikipedia site:

   http://en.wikipedia.org/wiki/Legendre_function

The 'hypergeom' function is in the Symbolic Toolbox.

(Note: I have never done this myself, so you are on your own in this endeavor.)