If you want to do #QuantumMechanics in #HigherDimensions then you need to know about associated Gegenbauer polynomials. Since there is no good reference on the web for these, I put together a presentation of Legendre, Gegenbauer and Jacobi polynomials to show how to derive their series expansions, Rodrigues formulas and differential equations:

https://analyticphysics.com/Special%20Functions/Hypergeometric%20Orthogonal%20Polynomials.htm

Lots of tedious detail that ultimately simplifies nicely. Suspect I'm missing something important here...

#Physics #SpecialFunctions