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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 tanh-1(z)





http://functions.wolfram.com/01.14.16.0246.01









  


  










Input Form





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










Standard Form





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MathML Form







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<mrow> <mi> &#8520; </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> y </mi> </mrow> </msqrt> </mrow> <msqrt> <mrow> <mi> y </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <arctan /> <ci> x </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arctanh /> <ci> y </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <pi /> <apply> <floor /> <apply> <times /> <apply> <plus /> <apply> <arg /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> x </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arg /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> x </ci> </apply> </apply> </apply> </apply> </apply> <pi /> </apply> 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type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <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> </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> <floor /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <imaginary /> <apply> <ln /> <apply> <plus /> <ci> y </ci> <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> <floor /> <apply> <times /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <imaginary /> <apply> <ln /> <apply> <times 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<times /> <cn type='integer'> -1 </cn> <ci> y </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> y </ci> <cn type='integer'> 1 </cn> </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





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