Hermite polynomials #
This file defines
Polynomial.hermite n, the
nth probabilists' Hermite polynomial.
Main definitions #
Polynomial.hermite n: the
nth probabilists' Hermite polynomial, defined recursively as a
Polynomial.hermite_succ: the recursion
hermite (n+1) = (x - d/dx) (hermite n)
Polynomial.coeff_hermite_explicit: a closed formula for (nonvanishing) coefficients in terms of binomial coefficients and double factorials.
(hermite n).coeff kis zero.
Polynomial.coeff_hermite_of_even_add: a closed formula for
(hermite n).coeff kwhen
n+kis even, equivalent to
Polynomial.monic_hermite: for all
hermite nis monic.
Polynomial.degree_hermite: for all
hermite nhas degree