Differentiate spherical harmonics FastTransforms.jl


I am trying to differentiate spherical harmonic expansion by first converting to bivariate Fourier series using the package FastTransforms.jl.

Here’s what I have so far:

julia> N=15;

julia> M=2*N-1;

julia> C=sphrandn(Float64, N, M);

julia> CF=sph2fourier(C); convert to Fourier series

Question: How do I differentiate with respect to theta (the polar angle) in the Fourier coefficient space? For normal fft, I can multiply the Fourier coeffs by fftfreq.