Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
orthogonal polynomials |
| gptkbp:alsoKnownAs |
Chebyshev polynomial of the second kind
|
| gptkbp:application |
numerical analysis
approximation theory spectral methods |
| gptkbp:definedIn |
real numbers
|
| gptkbp:degree |
n
|
| gptkbp:domain |
[-1,1]
|
| gptkbp:explicitFormula |
U_n(x) = sin((n+1)arccos(x))/sin(arccos(x))
|
| https://www.w3.org/2000/01/rdf-schema#label |
Chebyshev U
|
| gptkbp:initialCondition |
U_0(x) = 1
U_1(x) = 2x |
| gptkbp:namedAfter |
gptkb:Pafnuty_Chebyshev
|
| gptkbp:orthogonalWithRespectTo |
weight function sqrt(1-x^2) on [-1,1]
|
| gptkbp:polynomialFamily |
gptkb:Chebyshev_polynomials
|
| gptkbp:recurrence |
U_{n+1}(x) = 2x U_n(x) - U_{n-1}(x)
|
| gptkbp:relatedTo |
gptkb:Chebyshev_T
|
| gptkbp:sequence |
A001353
|
| gptkbp:variant |
x
|
| gptkbp:bfsParent |
gptkb:Chebyshev_(crater)
|
| gptkbp:bfsLayer |
7
|