ѦਹѤʞ Relations between special functions:
https://www.johndcook.com/blog/special_function_diagram/
#maths #mathematics #functions #SpecialFunctions #JohnDCook #math
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@Perl One of the things I learned tonight is that the #specialfunctions and #statisticaldistributions library beating inside #rstats is available as a standalone version. While this speaks volumes of the portability of #clang, it also creates opportunities for transporting a significant chunk of R's functionalities into other languages, e.g. by writing swig interfaces. This may be an interesting #perl #pdl project
from "Special Functions of Mathematical Physics and Chemistry" by Ian N Sneddon (1956)
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...
analyticphysics.comHypergeometric Orthogonal Polynomials