MAINT: special: refactor C++ legendre and spherical harmonics #20539
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This is a work in progress PR, looking at best practices for special functions defined by recurrence relations. In particular, the focus is on the Legendre functions and spherical harmonics.
Essentially, for all these special functions defined by recurrence relations, we want to support a variety of possibilities. Computing and returning just the value itself, computing and storing all the values through the recurrence, applying a transformation to get the derivative, and who knows what else. Can we do it simply without writing the same algorithm many times?