Difference between revisions of "Chebyshev U"
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The Chebyshev polynomials of the second kind are orthogonal polynomials defined by | The Chebyshev polynomials of the second kind are orthogonal polynomials defined by | ||
| − | $$U_n(x) = \sin(n \mathrm{arcsin}(x)) | + | $$U_n(x) = \sin(n \mathrm{arcsin}(x)),$$ |
| + | where $\sin$ denotes [[sine]] and $\mathrm{arcsin}$ denotes [[arcsin]]. | ||
=Properties= | =Properties= | ||
| − | + | [[Orthogonality of Chebyshev U on (-1,1)]]<br /> | |
| + | [[Relationship between Chebyshev U and hypergeometric 2F1]]<br /> | ||
| + | [[Relationship between Chebyshev U and Gegenbauer C]]<br /> | ||
| − | + | =References= | |
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{{:Orthogonal polynomials footer}} | {{:Orthogonal polynomials footer}} | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 22:40, 19 December 2017
The Chebyshev polynomials of the second kind are orthogonal polynomials defined by $$U_n(x) = \sin(n \mathrm{arcsin}(x)),$$ where $\sin$ denotes sine and $\mathrm{arcsin}$ denotes arcsin.
Properties
Orthogonality of Chebyshev U on (-1,1)
Relationship between Chebyshev U and hypergeometric 2F1
Relationship between Chebyshev U and Gegenbauer C
