The Chebyshev polynomials of the first (*T _{n }* and second (

or can be constructed using the three term recurrence relation:

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

The **ChebyshevSum** subroutine calculates the sum of Chebyshev polynomials *c _{0 }T_{0 }(x) + c_{1 }T_{1 }(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

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

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