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Package legndr (in legndr.i) -

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DOCUMENT legndr(l,m, x) return the associated Legendre function Plm(x). The X may be an array (-1<=x<=1), but L and M (0<=M<=L) must be scalar values. For m=0, these are the Legendre polynomials Pl(x). Relation of Plm(x) to Pl(x): Plm(x) = (-1)^m (1-x^2)^(m/2) d^m/dx^m(Pl(x)) Relation of Plm(x) to spherical harmonics Ylm: Ylm(theta,phi)= sqrt((2*l+1)(l-m)!/(4*pi*(l+m)!)) * Plm(cos(theta)) * exp(1i*m*phi)

SEE ALSO: ylm_coef

DOCUMENT ylm_coef(l,m) return sqrt((2*l+1)(l-m)!/(4*pi*(l+m)!)), the normalization coefficient for spherical harmonic Ylm with respect to the associated Legendre function Plm. In this implementation, 0<=m<=l; use symmetry for m<0, or use sines and cosines instead of complex exponentials. Unlike Plm, array L and M arguments are permissible here. WARNING: These get combinitorially small with large L and M; probably Plm is simultaneously blowing up and should be normalized directly in legndr if what you want is Ylm. But I don't feel like working all that out -- if you need large L and M results, you should probably be working with some sort of asymptotic form anyway...

SEE ALSO: legndr