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ArcCot






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCot[z] > Transformations > Related transformations > Sums involving the direct function > Involving tanh-1(z)





http://functions.wolfram.com/01.16.16.0213.01









  


  










Input Form





ArcCot[x] + ArcTanh[y] == Pi Floor[(-Arg[1 - I/x] + Arg[1 + I/x] + Pi)/(2 Pi)] - 2 I Pi (Floor[(-Arg[((x - I)/(x + I))^(I/2)/Sqrt[1 - y]] - (1/2) Arg[y + 1] + Pi)/(2 Pi)] + Floor[(Pi - Im[Log[((x - I)/(x + I))^(I/2)/Sqrt[1 - y]]])/(2 Pi)] + Floor[(Pi - (1/2) Im[Log[y + 1]])/(2 Pi)]) - 2 I Pi (Floor[(-Arg[((x - I)/(x + I))^(I/2)] + (1/2) Arg[1 - y] + Pi)/ (2 Pi)] + Floor[((1/2) Im[Log[1 - y]] + Pi)/(2 Pi)] + Floor[(Pi - (1/2) Re[Log[(x - I)/(x + I)]])/(2 Pi)]) + Log[(((x - I)/(x + I))^(I/2) Sqrt[y + 1])/Sqrt[1 - y]]










Standard Form





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MathML Form







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/> <apply> <plus /> <ci> y </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arg /> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> x </ci> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> x </ci> <imaginaryi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> y </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <pi /> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> 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</cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> y </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> y </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02