dot-CalcLegendre: Compute Associated Legendre Functions Given Sequence of...

In wmm: World Magnetic Model

Description

Procedure that computes the associated Legendre function, P_{n,m}(mu), given a sequence of (degree, order) indices and function argument mu. This is computed via a closed-form equation.

Usage

.CalcLegendre(mu)

Arguments

mu	Function argument to P_{n,m}(mu)

Details

The underlying equation used is:

P(x, n, m)=(-1)^m * 2^n * (1-x^2)^(m/2) * sum(for m <= k <= n: k!/(k-m)! * x^(k-m) * choose(n, k) * choose((n+k-1)/2, n))

wmm documentation built on Sept. 6, 2021, 9:10 a.m.