Hermite polynomials

The Hermite polynomials can be defined as

or can be constructed using the three term recurrence relation:

H₀ (x) = 1,
H₁ (x) = 2x.
H_n+1 (x) = 2xH_n (x) - 2nH_n-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_n (x) for any given x.

The HermiteSum subroutine calculates the sum of Hermite polynomials c₀ H₀ (x) + c₁ H₁ (x) + ... + c_n H_n (x) using Clenshaw's recurrence formula.

The HermiteCoefficients subroutine can represent H_n (x) as a sum of powers of x: c₀  + c₁ x + ... + c_n x ⁿ.

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