Chebyshev polynomials of the first kind
GPTKB entity
Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
orthogonal polynomials |
| gptkbp:application |
numerical analysis
approximation theory minimax approximation spectral methods |
| gptkbp:category |
orthogonal polynomials
special functions |
| gptkbp:degree |
n
|
| gptkbp:differential |
(1-x^2)y'' - x y' + n^2 y = 0
|
| gptkbp:explicitFormula |
T_n(x) = cos(n arccos(x))
|
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:firstPolynomial |
T_0(x) = 1
|
| https://www.w3.org/2000/01/rdf-schema#label |
Chebyshev polynomials of the first kind
|
| gptkbp:leadingCoefficient |
2^{n-1} (for n ≥ 1)
|
| gptkbp:namedAfter |
gptkb:Pafnuty_Chebyshev
|
| gptkbp:orthogonalOn |
[-1, 1]
|
| gptkbp:recurrence |
T_{n+1}(x) = 2x T_n(x) - T_{n-1}(x)
|
| gptkbp:relatedTo |
gptkb:Chebyshev_polynomials_of_the_second_kind
|
| gptkbp:rootWord |
cos((2k-1)π/(2n)), k=1,...,n
|
| gptkbp:secondPolynomial |
T_1(x) = x
|
| gptkbp:symbol |
T_n(x)
|
| gptkbp:weight |
(1-x^2)^{-1/2}
|
| gptkbp:bfsParent |
gptkb:Chebyshev_series
gptkb:Chebyshev_H gptkb:Chebyshev_polynomial |
| gptkbp:bfsLayer |
8
|