Difference between revisions of "Chebyshev T"

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(Properties)
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[[Relationship between Chebyshev T and hypergeometric 2F1]]<br />
 
[[Relationship between Chebyshev T and hypergeometric 2F1]]<br />
 
[[Relationship between Chebyshev T and Gegenbauer C]]<br />
 
[[Relationship between Chebyshev T and Gegenbauer C]]<br />
[[Orthogonal polynomials footer]]<br />
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{{:Orthogonal polynomials footer}}
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 22:31, 19 December 2017

Chebyshev polynomials of the first kind are orthogonal polynomials defined for $n=0,1,2,\ldots$ by $$T_n(x) = \cos(n \mathrm{arccos}(x)),$$ where $\cos$ denotes cosine and $\mathrm{arccos}$ denotes arccos.

Properties

T_(n+1)(x)-2xT_n(x)+T_(n-1)(x)=0
Orthogonality of Chebyshev T on (-1,1)
Relationship between Chebyshev T and hypergeometric 2F1
Relationship between Chebyshev T and Gegenbauer C

Orthogonal polynomials