Yorick Standard Library

Package legndr (in legndr.i) -

Index of documented functions or symbols:

L

Y

legndr

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)

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...