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variants of this functions
ChebyshevT






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevT[nu,z] > Representations through more general functions > Through hypergeometric functions > Involving 2F1





http://functions.wolfram.com/07.04.26.0028.01









  


  










Input Form





ChebyshevT[\[Nu], z] == 2^(\[Nu] - 1) (-z^2)^(\[Nu]/2) (Cos[(Pi \[Nu])/2] + (z/Sqrt[-z^2]) Sin[(Pi \[Nu])/2]) Hypergeometric2F1[-(\[Nu]/2), (1 - \[Nu])/2, 1 - \[Nu], 1/z^2] + (2^(-\[Nu] - 1) (Cos[(Pi \[Nu])/2] - (z/Sqrt[-z^2]) Sin[(Pi \[Nu])/2]) Hypergeometric2F1[\[Nu]/2, (1 + \[Nu])/2, 1 + \[Nu], 1/z^2])/ (-z^2)^(\[Nu]/2) /; !IntervalMemberQ[Interval[{-1, 0}], z] && !Element[2 \[Nu], Integers]










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