Here are some functions for constructing individual members of certain families of orthogonal polynomials.
Let n be a non-negative integer, and x a ring element
(typically an indeterminate or a number). The functions below
evaluate the corresponding polynomial at x: if x is an
indeterminate then the polynomial itself is returned.
ChebyshevPoly(n,x) Chebyshev polynomial of 1st kind
ChebyshevPoly2(n,x) Chebyshev polynomial of 2nd kind
HermitePoly(n,x) Hermite polynomial (physics)
HermitePoly2(n,x) Hermite polynomial (probability)
LaguerrePoly(n,x) Laguerre polynomomial multiplied by factorial(n)
DicksonPoly(x,n,alpha) Dickson polynomial of 1st type not orthog
DicksonPoly2(x,n,alpha) Dickson polynomial of 2nd type not orthog
Some of the Chebyshev functions are not used, but I left them there in case they ever become useful.
The dispatch functions for Hermite polynomials have not been tested; so I do not know if the criterion for choosing between "explicit" and "iterative" implementations actually makes any sense.
2017