I was implementing the IGRF-13 Geomagnetic model, and a parts of the equation (3 a, b, and c) requires calculating the Associated Legendre polynomials with Schmidt quasi-Normalization and its partial derivatives.
For the Associated Legendre polynomials, I used the function Legendre(n, x, 'sch') and it works perfectly. But now how would I calculate their partial derivatives?
Equations 19 a, b, and c provides some recursive formulae, but I am not getting the correct result possibly because I might have implemented them incorrectly. Even the sample MATLAB code provided in the paper is not producing the proper results.
I would really appreciate it if someone could provide a proper implementation for calculating the Partial derivatives of these Legendre Polynomials.