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variants of this functions
ChebyshevT






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevT[nu,z] > Series representations > Generalized power series > Expansions on branch cuts > For the function itself





http://functions.wolfram.com/07.04.06.0043.01









  


  










Input Form





ChebyshevT[\[Nu], z] \[Proportional] Sin[Pi \[Nu]] Sqrt[1 - x^2] Exp[Pi I Floor[Arg[z - x]/(2 Pi)]] ChebyshevU[\[Nu] - 1, -x] + Cos[Pi \[Nu]] (-2 I I^Floor[Arg[z - x]/(2 Pi)] Floor[Arg[z - x]/(2 Pi)] + Exp[Pi I Floor[Arg[z - x]/(2 Pi)]]) ChebyshevT[\[Nu], -x] + (((\[Nu] Sin[Pi \[Nu]])/Sqrt[1 - x^2]) Exp[Pi I Floor[Arg[z - x]/(2 Pi)]] ChebyshevT[\[Nu], -x] - \[Nu] Cos[Pi \[Nu]] (-2 I I^Floor[Arg[z - x]/(2 Pi)] Floor[Arg[z - x]/(2 Pi)] + Exp[Pi I Floor[Arg[z - x]/(2 Pi)]]) ChebyshevU[\[Nu] - 1, -x]) (z - x) + \[Ellipsis] /; (z -> x) && Element[x, Reals] && x < -1










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





© 1998- Wolfram Research, Inc.