Additional combinatorial functions and polynomials

[spinkney]

This is a request for additional polynomial functions in Stan. I think it's as easy as wrapping boost functions from boost sf_poly https://www.boost.org/doc/libs/1_75_0/libs/math/doc/html/math_toolkit/sf_poly/ the relevant hpp files are at https://github.com/boostorg/math/tree/develop/include/boost/math/special_functions.

That contains the following: With derivatives

• [ ] ~~gegenbauer.html~~
• [ ] jacobi.html
• [ ] ~~legendre.html~~
• [ ] ~~chebyshev.html~~
• [ ] cardinal_b_splines.html

Without

• [ ] legendre_stieltjes.html
• [ ] hermite.html
• [ ] sph_harm.html
• [ ] laguerre.html

A closed issue about chebyshev polynomials (issue 37 stan-dev) where the OP wrote it themselves and didn't need it in Stan.

I'm most interested in getting jacobi, legendre, hermite and laguerre.

Updates: Legendre, Gegenbauer, and Chebyshev can all be derived from jacobi see https://people.sc.fsu.edu/~jburkardt/cpp_src/jacobi_polynomial/jacobi_polynomial.html.

Hermite polynomial has an easy derivative

Laguerre as well