Difference between revisions of "Chebyshev T"
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=Properties= | =Properties= | ||
[[T_(n+1)(x)-2xT_n(x)+T_(n-1)(x)=0]]<br /> | [[T_(n+1)(x)-2xT_n(x)+T_(n-1)(x)=0]]<br /> | ||
| − | [[Orthogonality of Chebyshev T on (-1,1)]] | + | [[Orthogonality of Chebyshev T on (-1,1)]]<br /> |
| − | + | [[Relationship between Chebyshev T and hypergeometric 2F1]]<br /> | |
| − | + | [[Relationship between Chebyshev T and Gegenbauer C]]<br /> | |
| − | + | [[Orthogonal polynomials footer]]<br /> | |
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[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 22:30, 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 footer
