Can someone please provides me with the recursion relations of Associated Legendre Polynomials when using Schmidt quasi-normalization? I need that in the context of Geomagnetism to obtain the Spherical Harmonics coefficients g and h.
FYI, the usual reference relied on for the equations used in geomagnetism is:
- Langel, R. A. "Chapter four: Main field." Geomagnetism, edited by JA Jacobs (1987).
If it wasn't for lockdown I'd have copied from the book locked in my office to make sure I got it right...but until someone corrects me...
The Schmidt quasi/semi-normalisations for the associated Legendre polynomials are given by these recursions, in the form you'd actually use for calculations typically:
Note that if you use Schmidt normalisation of Legendre polynomials from a given software language to do calculations, you do not want to include the Condon-Shortley phase factor of . So check if it is included in the Legendre polynomial and/or normalisation formula.
Edit: Some links to open source geomagnetism compatible software for calculating Schmidt normalised associated Legendre polynomials.