This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# ChebyshevT

 ChebyshevTgives 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 Chebyshev polynomial:
Compute the Chebyshev polynomial:
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 Scope   (6)
Evaluate for complex arguments and orders:
Evaluate for large orders:
Evaluate to high precision:
Simple cases give exact symbolic results even for arbitrary order:
ChebyshevT can be applied to power series:
ChebyshevT can be applied to Interval:
 Applications   (2)
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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