treams.special.vsh_Y¶
- treams.special.vsh_Y(l, m, theta, phi) = <ufunc 'vsh_Y'>¶
Vector spherical harmonic Y in spherical coordinates
The vector spherical harmonics can be defined by \(\boldsymbol Y_{lm}(\theta, \varphi) = \boldsymbol{\hat r} \times \boldsymbol X_{lm}(\theta, \varphi)\) using
treams.special.vsh_X(). Alternatively, it can can be expressed as\[\boldsymbol Y_{lm}(\theta, \varphi) = \mathrm i \sqrt{\frac{2 l + 1}{4 \pi l (l + 1)} \frac{(l - m)!}{(l + m)!}} \left(\tau_{lm}(\theta, \varphi) \boldsymbol{\hat\theta} + \mathrm i \pi_{lm}(\theta, \varphi) \boldsymbol{\hat\varphi}\right)\]with the angular functions
treams.special.pi_fun()andtreams.special.tau_fun().- Parameters:
l (int, array_like) – Degree \(l \geq 0\)
m (int, array_like) – Order \(|m| \leq l\)
theta (float or complex, array_like) – Polar angle
phi (float, array_like) – Azimuthal angle
- Returns:
complex, 3-array