Spherical Harmonic Function

Let $n$ be a non-negative integer, $m$ an integer number, $\theta$ a real number and $0\leqslant\theta\leqslant\pi$, $\phi$ a real number and $0\leqslant\phi\leqslant 2\pi$, this application evaluates the spherical harmonic function \[ Y_n^m(\theta,\phi) = \sqrt{\frac{2n+1}{4\pi}\frac{(n-m)!}{(n+m)!}}P_n^m(\cos\theta)\mathrm{e}^{im\phi} \] where $P_n^m(\cos\theta)$ is the associate Legendre polynomial.

Spherical Harmonic Function Calculator