Definition:Chebyshev Polynomials/First Kind

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The Chebyshev polynomials of the first kind are defined as polynomials such that:

\(\ds \map {T_n} {\cos \theta}\) \(=\) \(\ds \map \cos {n \theta}\)

Recursive Definition

$\map {T_n} x = \begin{cases}

1 & : n = 0 \\ x & : n = 1 \\ 2 x \map {T_{n - 1} } x - \map {T_{n - 2} } x & : n > 1 \end{cases}$

Also known as

The Chebyshev polynomials can also be seen as Tchebyshev polynomials.

Other transliterations exist.

Some sources define only the Chebyshev polynomials of the first kind, referring to them merely as Chebyshev polynomials.

Also see

Source of Name

This entry was named for Pafnuty Lvovich Chebyshev.