section of routines in legndr.i

functions in legndr.i -

 
 
 
legndr


             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  
 
 
 
ylm_coef


             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