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mathematical physics > special function > hypergeometric function > Chebyshev polynomial

mathematical analysis > functional analysis > special function > hypergeometric function > Chebyshev polynomial

... > function > elementary function > polynomial > orthogonal polynomials > Chebyshev polynomial

algebra > polynomial > orthogonal polynomials > Chebyshev polynomial

Terme préférentiel

Chebyshev polynomial

The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as ${\\displaystyle T_{n}(x)}$ and ${\\displaystyle U_{n}(x)}$ . They can be defined in several equivalent ways, one of which starts with trigonometric functions:
The Chebyshev polynomials of the first kind ${\\displaystyle T_{n}}$ are defined by:

${\\displaystyle T_{n}(\\cos \ heta )=\\cos(n\ heta ).}$

Similarly, the Chebyshev polynomials of the second kind ${\\displaystyle U_{n}}$ are defined by:

${\\displaystyle U_{n}(\\cos \ heta )\\sin \ heta =\\sin {\ig (}(n+1)\ heta {\ig )}.}$

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Chebyshev_polynomials)

approximation theory

polynôme de Tchebychev

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