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variants of this functions
ChebyshevT






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevT[nu,z] > Series representations > Generalized power series > Expansions at nu==0 > For the function itself





http://functions.wolfram.com/07.04.06.0038.01









  


  










Input Form





ChebyshevT[\[Nu], z] == Subscript[F, Infinity][z, \[Nu]] /; Subscript[F, n][z, \[Nu]] == Sum[((-1)^k ArcCos[z]^(2 k) \[Nu]^(2 k))/ (2 k)!, {k, 0, n}] == ChebyshevT[\[Nu], z] + (((-1)^n Sqrt[Pi] ArcCos[z]^(2 + 2 n) \[Nu]^(2 + 2 n))/2^(2 n + 2)) HypergeometricPFQRegularized[{1}, {3/2 + n, 2 + n}, -((ArcCos[z]^2 \[Nu]^2)/4)] && Element[n, Integers] && n >= 0










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





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