Chebyshev polynomials of the second kind
GPTKB entity
Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
orthogonal polynomials
|
| gptkbp:abbreviation |
U_n(x)
|
| gptkbp:application |
numerical analysis
approximation theory spectral methods |
| gptkbp:definedIn |
[-1, 1]
|
| gptkbp:degree |
n
|
| gptkbp:explicitFormula |
U_n(x) = sin((n+1) arccos x) / sqrt(1-x^2)
|
| gptkbp:firstPolynomial |
U_0(x) = 1
|
| https://www.w3.org/2000/01/rdf-schema#label |
Chebyshev polynomials of the second kind
|
| gptkbp:namedAfter |
gptkb:Pafnuty_Chebyshev
|
| gptkbp:orthogonalWithRespectTo |
weight function sqrt(1-x^2)
|
| gptkbp:recurrence |
U_{n+1}(x) = 2x U_n(x) - U_{n-1}(x)
|
| gptkbp:relatedTo |
gptkb:Chebyshev_polynomials_of_the_first_kind
|
| gptkbp:secondPolynomial |
U_1(x) = 2x
|
| gptkbp:sequence |
A053120
|
| gptkbp:bfsParent |
gptkb:Chebyshev_series
gptkb:Chebyshev_T gptkb:Chebyshev_polynomial |
| gptkbp:bfsLayer |
8
|