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ArcSinh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSinh[z] > Transformations > Related transformations > Differences involving the direct function > Involving cot-1(z)





http://functions.wolfram.com/01.25.16.0189.01









  


  










Input Form





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










Standard Form





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MathML Form







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/> <ci> y </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </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