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ArcSinh




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.25.27.1728.01









  


  








Input Form





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








Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> sinh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mfrac> <mrow> <mi> z </mi> <mo> - </mo> <msqrt> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mfrac> </msqrt> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mfrac> <mi> &#960; </mi> <mrow> <mn> 4 </mn> <mtext> </mtext> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </mrow> </msqrt> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; 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Rule Form





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





2003-08-21