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ArcSec






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSec[z] > Representations through equivalent functions > With related functions > Involving cosh-1 > Involving sec-1((2z)1/2/(z-(z2-1)1/2)1/2) > Involving sec-1((2z)1/2/(z-(z2-1)1/2)1/2) and cosh-1(1/z)





http://functions.wolfram.com/01.18.27.1458.01









  


  










Input Form





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










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> sec </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> <msqrt> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> <mo> - </mo> <mrow> <mfrac> <mrow> <msqrt> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mfrac> <mo> &#8290; 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Rule Form





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





2003-08-21