This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

ChebyshevU

ChebyshevU
gives the Chebyshev polynomial of the second kind .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Explicit polynomials are given for integer n.
  • .
  • For certain special arguments, ChebyshevU automatically evaluates to exact values.
  • ChebyshevU can be evaluated to arbitrary numerical precision.
  • ChebyshevU has a branch cut discontinuity in the complex z plane running from to for noninteger n.
Compute the 10^(th) ChebyshevU polynomial:
Compute the 10^(th) ChebyshevU polynomial:
In[1]:=
Click for copyable input
Out[1]=
 
In[1]:=
Click for copyable input
Out[1]=
Evaluate for complex arguments and orders:
Evaluate for large orders:
Evaluate to high precision:
ChebyshevU threads element-wise over the list:
Simple cases give exact symbolic results even for arbitrary order:
TraditionalForm formatting:
ChebyshevU can be applied to power series:
ChebyshevU can be applied to Interval:
Approximate a function on the interval :
Build a curve that passes through given points:
Light amplitude transmission through layers of glass:
Get the list of coefficients in a ChebyshevU polynomial:
Use FunctionExpand to expand through trigonometric functions:
Derivative of ChebyshevU with respect to :
Cancellations in the polynomial form may lead to inaccurate numerical results:
Evaluate the function directly:
New in 1