Do you have
function y = spharm( ltab, mtab, theta, phi )
% SPHARM - Spherical harmonics.
%
% Usage :
% y = spharm( ltab, mtab, theta, phi )
% Input
% ltab : table of spherical harmonic degrees
% mtab : table of spherical harmonic orders
% theta : polar angle
% phi : azimuthal angle
% Output
% y : spherical harmonic
% convert to column and row vectors
[ ltab, mtab ] = deal( reshape( ltab, [], 1 ), reshape( mtab, [], 1 ) );
[ theta, phi ] = deal( reshape( theta, 1, [] ), reshape( phi, 1, [] ) );
% table of factorials
ftab = factorial( 0 : ( 2 * max( ltab ) + 1 ) );
% dimension output
y = zeros( length( ltab ), length( theta ) );
% loop over unique ltab values
for l = reshape( unique( ltab ), 1, [] )
% full table of Legendre functions
ptab = legendre( l, cos( theta ) );
% index to entries with degree L and
% with angular order smaller than angular order
ind = find( ltab == l );
ind = ind( abs( mtab( ind ) ) <= l );
for i = reshape( ind, 1, [] )
% corresponding spherical order (only absolute value considered first)
m = mtab( i );
% prefactor for spherical harmonics
c = sqrt( ( 2 * l + 1 ) / ( 4 * pi ) * ...
ftab( l - abs( m ) + 1 ) / ftab( l + abs( m ) + 1 ) );
% spherical harmonics
y( i, : ) = c * ptab( abs( m ) + 1, : ) .* exp( 1i * abs( m ) * phi );
% correct for negative orders
if ( m < 0 ), y( i, : ) = ( - 1 ) ^ m * conj( y( i, : ) ); end
end
end
end
on your MATLAB path ?
And conj(Ylm) in your integral is just a constant vector that won't depend on t and the length of which is incompatible with the t-vector supplied by the "integral"-function.
