The Hermite polynomials can be defined as
or can be constructed using the three term recurrence relation:
H0(x) = 1,The recurrence relation given above is the most efficient way to calculate the Hermite polynomial. The HermiteCalculate subroutine uses this relation to calculate Hn(x) for any given x.
The HermiteSum subroutine calculates the sum of Hermite polynomials c0H0(x) + c1H1(x) + ... + cnHn(x) using Clenshaw's recurrence formula.
The HermiteCoefficients subroutine can represent Hn(x) as a sum of powers of x: c0 + c1x + ... + cnxn.
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