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variants of this functions
ChebyshevU






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.05.06.0049.01









  


  










Input Form





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










Standard Form





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MathML Form







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</ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> </apply> </apply> <apply> <ci> O </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> x </ci> <reals /> </apply> <apply> <lt /> <ci> x </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





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