Hermite polynomials

The Hermite polynomials can be defined as

or can be constructed using the three term recurrence relation:

H(x) = 1,
H(x) = 2x.
Hn+1 (x) = 2xH(x) - 2nHn-1 (x)

Unit description

The recurrence relation given above is the most efficient way to calculate the Hermite polynomial. The HermiteCalculate subroutine uses this relation to calculate H(x) for any given x.

The HermiteSum subroutine calculates the sum of Hermite polynomials cH(x) + cH(x) + ... + cH(x) using Clenshaw's recurrence formula.

The HermiteCoefficients subroutine can represent H(x) as a sum of powers of x: c + cx + ... + cx n.

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