User talk:71.184.153.51

Your 6th recurrence relation states that

sqrt(1-x^2) Pl,m(x) = [ Pl+1,m+1(x) - Pl-1,m+1(x) ] / (2 l + 1)

When I apply this for m=-1, with l=1 or l=2, I find that the sign is incorrect. For l=1, I get

(1-x^2)/2 = -(1-x^2)/2

For l=2, I get

x (1-x^2)/2 = - x (1-x^2)/2.

Is there a caveat regarding application of the recurrence formula for negative m?

Regards, Lex