chaosmagpy.model_utils.legendre_poly¶
- chaosmagpy.model_utils.legendre_poly(nmax, theta)[source]¶
Returns associated Legendre polynomials \(P_n^m(\cos\theta)\) (Schmidt quasi-normalized) and the derivative \(dP_n^m(\cos\theta)/d\theta\) evaluated at \(\theta\).
- Parameters:
- nmaxint, positive
Maximum degree of the spherical expansion.
- thetandarray, shape (…)
Colatitude in degrees \([0^\circ, 180^\circ]\) of arbitrary shape.
- Returns:
- Pnmndarray, shape (n, m, …)
Evaluated values and derivatives, grid shape is appended as trailing dimensions. \(P_n^m(\cos\theta)\) :=
Pnm[n, m, ...]
and \(dP_n^m(\cos\theta)/d\theta\) :=Pnm[m, n+1, ...]
References
Based on Equations 26-29 and Table 2 in:
Langel, R. A., “Geomagnetism - The main field”, Academic Press, 1987, chapter 4