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Mathematica > Mathematics and Algorithms > Mathematical Functions > Special Functions >

Built-in Mathematica Symbol

ChebyshevT

ChebyshevT[n, x]
gives the Chebyshev polynomial of the first kind

For certain special arguments, ChebyshevT automatically evaluates to exact values.

ChebyshevT[n, z] has a branch cut discontinuity in the complex z plane running from - to .

Compute the

Chebyshev polynomial:

Compute the

Chebyshev polynomial:

Evaluate for complex arguments and orders:

Evaluate for large orders:

Evaluate to high precision:

ChebyshevT threads element-wise over lists:

Simple cases give exact symbolic results even for arbitrary order:

ChebyshevT can be applied to power series:

ChebyshevT can be applied to Interval:

Plot the first 10 Chebyshev polynomials:

Find a minimax approximation to the function Clip[4 x]:

Derivative of ChebyshevT is expressed in terms of ChebyshevU:

Cancellations in the polynomial form may lead to inaccurate numerical results:

Evaluate the function directly: