The Hermite polynomials can be defined as

or can be constructed using the three term recurrence relation:

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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C#

C# 1.0 source.
hermite.csharp.zip - Hermite polynomials

C++

C++ source.
hermite.cpp.zip - Hermite polynomials
ablas.zip - optimized basic linear algebra subroutines with SSE2 support (for C++ sources only)

Delphi

Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
hermite.delphi.zip - Hermite polynomials

Visual Basic 6

Visual Basic 6 source.
hermite.vb6.zip - Hermite polynomials

Zonnon ^beta

Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
hermite.zonnon.zip - Hermite polynomials