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variants of this functions
ChebyshevU






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevU[nu,z] > Series representations > Asymptotic series expansions > Expansions at nu==infinity





http://functions.wolfram.com/07.05.06.0083.01









  


  










Input Form





ChebyshevU[\[Nu], z] \[Proportional] Piecewise[{{(1/2 - (I z)/(2 Sqrt[1 - z^2])) E^(I \[Nu] ArcCos[z]), -Pi < Arg[(\[Nu] + 1) ArcCos[z]] < 0}, {(1/2 + (I z)/(2 Sqrt[1 - z^2]))/E^(I \[Nu] ArcCos[z]), 0 < Arg[(\[Nu] + 1) ArcCos[z]] < Pi}}, Sin[(\[Nu] + 1) ArcCos[z]]/ Sqrt[1 - z^2]] /; (Abs[\[Nu]] -> Infinity)










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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