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ArcSin






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.12.16.0182.01









  


  










Input Form





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










Standard Form





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MathML Form







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










Rule Form





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





2007-05-02