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variants of this functions
ChebyshevT






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevT[nu,z] > Representations through more general functions > Through Meijer G > Classical cases for the direct function itself





http://functions.wolfram.com/07.04.26.0031.01









  


  










Input Form





ChebyshevT[\[Nu], z] == (-(\[Nu]/((-z^2)^((1 + \[Nu])/2) (4 Sqrt[Pi])))) (((-Sqrt[-z^2]) Cos[(Pi \[Nu])/2] + z Sin[(Pi \[Nu])/2]) MeijerG[{{1 - \[Nu]/2, (1 - \[Nu])/2}, {}}, {{0}, {-\[Nu]}}, -(1/z^2)] + (-z^2)^\[Nu] (Sqrt[-z^2] Cos[(Pi \[Nu])/2] + z Sin[(Pi \[Nu])/2]) MeijerG[{{(2 + \[Nu])/2, (1 + \[Nu])/2}, {}}, {{0}, {\[Nu]}}, -(1/z^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





© 1998- Wolfram Research, Inc.