Hello! 1. The problem statement, all variables and given/known data I want to evaluate the derivative of spherical harmonics with respect to the azimuthal angle and express it in terms of spherical harmonics. 2. Relevant equations and 3. The attempt at a solution I have calculated the derivative of the spherical harmonic with respect to the azimuthal angle. I know how to express the derivative of the spherical harmonic in terms of spherical harmonics for positive m. But I don't know how to do this for negative m. View attachment Spherical_Harmonics.pdf Thanks for your help.