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ArcSin




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.12.16.0143.01









  


  








Input Form





ArcSin[x] + I ArcTanh[y] == ArcSin[((-1)^Floor[1/2 - Arg[(x + I Sqrt[1 - x^2] y)/Sqrt[1 - y^2]]/Pi] (-Sqrt[1 - x^2] + I x y))/Sqrt[1 - y^2]] + (1/2) Pi ((-1)^Floor[1/2 - Arg[(x + I Sqrt[1 - x^2] y)/Sqrt[1 - y^2]]/Pi] + 2 (1 + (-1)^Floor[1/2 - Arg[(x + I Sqrt[1 - x^2] y)/Sqrt[1 - y^2]]/Pi]) Floor[(Arg[I x + Sqrt[1 - x^2]] + Arg[(I - I y)/Sqrt[1 - y^2]])/ (2 Pi)] - 2 (-1 + (-1)^Floor[1/2 - Arg[(x + I Sqrt[1 - x^2] y)/Sqrt[1 - y^2]]/Pi]) Floor[1/2 - (Arg[I x + Sqrt[1 - x^2]] + Arg[(I - I y)/Sqrt[1 - y^2]])/ (2 Pi)])








Standard Form





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MathML Form







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