Revision #737 → #1075 · back to history
addedChebyshev polynomials of the first kind (trigonometric)83baea43278e
addedChebyshev polynomials of the second kind (trigonometric)6ce81edf1efc
addedExtremal property of T_nbc2644a5af9d
addedRecurrence definition of T_nf413fc0a6de3
addedRecurrence definition of U_na4110237c5e6
addedTrigonometric definition (unique polynomials)eef1ed0c7f1c
addedDefinition via complex exponentiation5c3a86191cc1
addedT_n is a polynomial of degree n in x2fcfd0e9b6d8
addedDefinition extension outside [-1,1]7ef72e51379d
addedCommuting polynomials characterization6f6e6e714aee
addedPell equation definitiondaad1fda51fa
addedOrdinary generating function for T_nb518bddc68a2
addedExponential generating function for T_nb36559ee2c4e
addedPotential theory generating function88263275912d
addedGenerating functions for U_n1d8689f0779e
addedCorrespondence with Lucas sequencese996d3704783
addedMutual recurrence equationsd50e148060e3
addedSum formula76b6d8986125
addedRecurrence for derivative of T_n6bf4814bf2aa
addedTurán's inequalities5f6d9a9acd7a
addedIntegral relationsa14426381503
addedExplicit expressions from complex exponentiationf164807d4b8b
addedExplicit form in terms of monomials00335575927d
addedHypergeometric representation1d37ae58e4fe
addedU_n as sum of monomialsc22749a95b3b
addedSymmetry of Chebyshev polynomials375c7e0769bf
addedSimple roots in [-1,1]9b6f0f2b1d60
addedRoots of T_n (Chebyshev nodes)8b2195411404
addedExtrema of T_n6c50dd934a70
addedShabat polynomial property1aea629a37d3
addedExtrema of U_ne17ad6604856
addedMinimal polynomial of 2cos(2pi/n) case formulas19e55fcd1742
addedDerivatives via trigonometric form4dd652a9f6d8
addedL'Hôpital evaluation at endpointsaadcc936b69a
addedHigher derivatives identity7cc819beb19c
addedIntegration formula for T_n3ba4417be11a
addedIntegral of T_n in terms of T_n05f0f29b8d1e
addedProduct relation for T_n709d4247e87c
addedProduct relation for U_n32d8ea85ab80
addedComposition / nesting property18205aeb5f1d
addedDivisibility properties6f97637c88de
addedOrthogonality of T_n5f0a432db774
addedOrthogonality of U_n43755ac2ec61
addedChebyshev differential equationscb3af0446b9b
addedDiscrete orthogonality of T_nfa1d737ca732
addedDiscrete orthogonality of U_n at Chebyshev nodes2244d4211dc0
addedMinimal ∞-norm property of T_n97750c73eef1
addedEquioscillation theorem remark39a329320531
addedChebyshev as special case of Gegenbauer/Jacobi71ded3809440
addedChebyshev as special case of Dickson polynomials41ca1810cc3d
addedLissajous curve relation459df2c1f309
addedLegendre-Chebyshev relations5bde7f1b1024
addedDeterminant representation1d8b7e6f2c26
addedFirst few T_nb12041937e0b
addedFirst few U_nc5d716c0065a
addedOrthonormal basis in Sobolev space3095413efa36
addedChebyshev series convergence properties98bdb0987430
addedChebyshev expansion of log(1+x)8a9035f0b927
addedAnother expansion example6a0913c731f2
addedChebyshev–Gauss–Lobatto interpolation points2210f9a90f20
addedPolynomial in Chebyshev form0a1b1d88f00f
addedVieta–Lucas and Vieta–Fibonacci polynomialsf0f4dec8490c
addedShifted Chebyshev polynomials9fd048d9acd3
addedChebyshev polynomials of the third and fourth kinds3742fa7c1524
addedThird/fourth kind orthogonality and Jacobi proportionality1551a9b6e78d
addedCommon recurrence for four families32eff32f989a
addedFactorization via cyclotomic polynomials57213de372a6
addedIrreducibility of cyclotomic pre-polynomials9d176cb5b3f1
addedEven order modified Chebyshev polynomialsbf21cf2949f6
added4th order even order modified Chebyshev polynomialba783bc39bae