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ArcSech






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[z] > Representations through equivalent functions > With related functions > Involving sec-1 > Involving sech-1((2z)1/2/(z+a)1/2) > Involving sech-1((2z)1/2/(z+1)1/2) and sec-1(z)





http://functions.wolfram.com/01.30.27.1441.01









  


  










Input Form





ArcSech[Sqrt[2 z]/Sqrt[z + 1]] == (-((z Sqrt[1 - z])/2)) Sqrt[1/(1 - z)] Sqrt[-(1/z^2)] ArcSec[z] + (Pi/4) ((-z) Sqrt[-z^(-2)] - I Sqrt[1 - z] Sqrt[1/(1 - z)] - I + 2 I Sqrt[(z + 1)/z] Sqrt[z/(z + 1)] + z Sqrt[1 - z] Sqrt[1/(1 - z)] Sqrt[-(1/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> sech </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <msqrt> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msqrt> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mfrac> <mi> &#960; </mi> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> </msqrt> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <mn> 1 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </mfrac> </msqrt> </mrow> <mo> - </mo> <mi> &#8520; 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Rule Form





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





2003-08-21