The Chebyshev polynomials of the first (T_n  and second (U_n ) kinds can be defined by the trigonometric identity

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 Chebyshev polynomial. The ChebyshevCalculate subroutine uses this relation to calculate T_n (x) and/or U_n (x) for any given x.

The ChebyshevSum subroutine calculates the sum of Chebyshev polynomials c₀ T₀ (x) + c₁ T₁ (x) + ... + c_n T_n (x) using Clenshaw's recurrence formula.

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

The FromChebyshev subroutine can perform a conversion of a series of Chebyshev polynomials to a power series.

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C#

C# 1.0 source.
chebyshev.csharp.zip - Chebyshev polynomials

C++

C++ source.
chebyshev.cpp.zip - Chebyshev 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).
chebyshev.delphi.zip - Chebyshev polynomials

Visual Basic 6

Visual Basic 6 source.
chebyshev.vb6.zip - Chebyshev polynomials

Zonnon ^beta

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