Difference between revisions of "Chebyshev U"
From specialfunctionswiki
| Line 9: | Line 9: | ||
=References= | =References= | ||
| − | * {{BookReference|Special Functions for Scientists and Engineers|1968|W.W. Bell|prev=Chebyshev T|next= | + | * {{BookReference|Special Functions for Scientists and Engineers|1968|W.W. Bell|prev=Chebyshev T|next=T n(x)=(1/2)(x+i sqrt(1-x^2))^n+(1/2)(x-i sqrt(1-x^2))^n}}: $(7.2)$ |
{{:Orthogonal polynomials footer}} | {{:Orthogonal polynomials footer}} | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 19:15, 15 March 2018
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
References
- 1968: W.W. Bell: Special Functions for Scientists and Engineers ... (previous) ... (next): $(7.2)$
