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ArcSinh




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.25.27.1835.01









  


  








Input Form





ArcSinh[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])/(Sqrt[z^2] Sqrt[-1 - 2 z^2] Sqrt[-1 - z^2])) ArcCsch[1/z]








Standard Form





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MathML Form







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Rule Form





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





2003-08-21