treams.special.sph_harm

treams.special.sph_harm(m, l, phi, theta) = <ufunc 'sph_harm'>

Spherical harmonics of real and complex argument

Warning

In order to stay consistent with Scipy, the order of the arguments is kept the same. For most other functions, the postion of degree and order are swapped.

For complex argument the spherical harmonics are computed with

\[Y_{lm}(\theta, \varphi) = \sqrt{\frac{2l + 1}{4\pi}\frac{(l - m)!}{(l + m)!}} P_l^m(\cos\theta) \mathrm e^{\mathrm i m \varphi}\]

for real arguments scipy.special.sph_harm is used.

Parameters:

  • m (integer, array_like) – Order

  • l (integer, array_like) – Degree, non-negative

  • phi (float or complex, array_like) – Azimuthal angle

  • theta (float or complex, array_like) – Polar angle

Returns:

complex