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ArcCsch




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.29.27.1422.01









  


  








Input Form





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








Standard Form





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MathML Form







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</apply> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 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Rule Form





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





2003-08-21