Chebyshev P

GPTKB entity

Statements (19)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:alsoKnownAs Chebyshev polynomial of the first kind
gptkbp:category orthogonal polynomials
gptkbp:degree n
gptkbp:explicitFormula T_n(x) = cos(n arccos x)
gptkbp:firstPolynomial T_0(x) = 1
https://www.w3.org/2000/01/rdf-schema#label Chebyshev P
gptkbp:namedAfter gptkb:Pafnuty_Chebyshev
gptkbp:notation T_n(x)
gptkbp:orthogonalOn [-1, 1]
gptkbp:recurrence T_{n+1}(x) = 2x T_n(x) - T_{n-1}(x)
gptkbp:roots cos((2k-1)π/(2n)), k=1,...,n
gptkbp:secondPolynomial T_1(x) = x
gptkbp:usedIn numerical analysis
approximation theory
orthogonal polynomials
gptkbp:weight (1-x^2)^{-1/2}
gptkbp:bfsParent gptkb:Chebyshev_(crater)
gptkbp:bfsLayer 7