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variants of this functions
ArcTan






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.14.16.0240.01









  


  










Input Form





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










Standard Form





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MathML Form







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<imaginaryi /> <ci> x </ci> </apply> <cn type='integer'> 1 </cn> </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> <plus /> <ci> y </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </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





© 1998- Wolfram Research, Inc.