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The Legendre Functions and Legendre Polynomials are described in Abramowitz & Stegun, Chapter 8.
Modules
The following functions compute the associated Legendre Polynomials P_l^m(x).
Note that this function grows combinatorially with l and can overflow for l larger than about 150.
There is no trouble for small m, but overflow occurs when m and l are both large.
Rather than allow overflows, these functions refuse to calculate P_l^m(x) and return OvrFlw when they can sense that l and m are too big.
The Conical Functions P^\mu_{-(1/2)+i\lambda}(x) and Q^\mu_{-(1/2)+i\lambda} are described in Abramowitz & Stegun, Section 8.12.
The following spherical functions are specializations of Legendre functions which give the regular eigenfunctions of the Laplacian on a 3-dimensional hyperbolic space H3d. Of particular interest is the flat limit, \lambda \to \infty, \eta \to 0, \lambda\eta fixed.