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ChebyshevT

ChebyshevT
gives the Chebyshev polynomial of the first kind .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Explicit polynomials are given for integer n.
  • .
  • For certain special arguments, ChebyshevT automatically evaluates to exact values.
  • ChebyshevT can be evaluated to arbitrary numerical precision.
  • ChebyshevT has a branch cut discontinuity in the complex z plane running from to .
Compute the 10^(th) Chebyshev polynomial:
Compute the 10^(th) Chebyshev polynomial:
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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:
TraditionalForm formatting:
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:
Derivative of ChebyshevT is expressed in terms of ChebyshevU:
Cancellations in the polynomial form may lead to inaccurate numerical results:
Evaluate the function directly:
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