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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 c0 H0 (x) + c1 H1 (x) + ... + cn Hn (x) using Clenshaw's recurrence formula.
The HermiteCoefficients subroutine can represent Hn (x) as a sum of powers of x: c0 + c1 x + ... + cn x n.
This article is intended for personal use only.
C# source.
C++ source.
C++ source. MPFR/GMP is used.
GMP source is available from gmplib.org. MPFR source is available from www.mpfr.org.
FreePascal version.
Delphi version.
VB.NET version.
VBA version.
Python version (CPython and IronPython are supported).
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