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ChebyshevU[n, x]
gives the Chebyshev polynomial of the second kind U_n(x).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Explicit polynomials are given for integer n.
  • U_n(cos theta)=sin[(n+1)theta]/sin theta.
  • For certain special arguments, ChebyshevU automatically evaluates to exact values.
  • ChebyshevU can be evaluated to arbitrary numerical precision.
  • ChebyshevU[n, z] has a branch cut discontinuity in the complex z plane running from - to -1 for non-integer n.
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