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ArcSinh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSinh[z] > Representations through equivalent functions > With related functions > Involving csc-1 > Involving sinh-1(z) > Involving sinh-1(z) and csc-1(1/2 z (-z2-1)1/2)





http://functions.wolfram.com/01.25.27.0846.01









  


  








Input Form





ArcSinh[z] == (Pi/4) (-(Sqrt[-z^2]/z) - I Sqrt[I/z] Sqrt[(-I) z] Sqrt[1/(1 - I Sqrt[2] z)] Sqrt[1 - I Sqrt[2] z] + I Sqrt[-(I/z)] Sqrt[I z] Sqrt[1/(1 + I Sqrt[2] z)] Sqrt[1 + I Sqrt[2] z] - Sqrt[z^2 + z^4]/(z Sqrt[-1 - z^2])) - (Sqrt[-1 - 2 z^2]/(2 z^2 Sqrt[1 + 2 z^2])) Sqrt[-(z^2/(-1 - z^2))] Sqrt[(-z^2) (-1 - z^2)] ArcCsc[1/(2 z Sqrt[-z^2 - 1])]








Standard Form





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MathML Form







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type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </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> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> 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Rule Form





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





2003-08-21