Difference between revisions of "Chebyshev T"
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=References= | =References= | ||
| + | * {{BookReference|Special Functions for Scientists and Engineers|1968|W.W. Bell|prev=findme|next=Chebyshev U}}: $(7.1)$ | ||
* {{BookReference|An Introduction to Orthogonal Polynomials|1978|T.S. Chihara|prev=Orthogonality of Chebyshev T on (-1,1)|next=findme}} $(1.4)$ (<i>note: calls them Tchebichef polynomials of the first kind</i>) | * {{BookReference|An Introduction to Orthogonal Polynomials|1978|T.S. Chihara|prev=Orthogonality of Chebyshev T on (-1,1)|next=findme}} $(1.4)$ (<i>note: calls them Tchebichef polynomials of the first kind</i>) | ||
Revision as of 19:00, 15 March 2018
Chebyshev polynomials of the first kind are orthogonal polynomials defined for $n=0,1,2,\ldots$ and $-1 \leq x \leq 1$ 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
References
- 1968: W.W. Bell: Special Functions for Scientists and Engineers ... (previous) ... (next): $(7.1)$
- 1978: T.S. Chihara: An Introduction to Orthogonal Polynomials ... (previous) ... (next) $(1.4)$ (note: calls them Tchebichef polynomials of the first kind)
