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ArcSech






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[z] > Complex characteristics > Real part





http://functions.wolfram.com/01.30.19.0001.01









  


  










Input Form





Re[ArcSech[x + I y]] == Log[Sqrt[(1/(x^2 + y^2)) (1 + Sqrt[1 - 2 x + x^2 + y^2] Sqrt[(1 + x)^2 + y^2] + 2 (1 + x) Sqrt[Sqrt[1 - 2 x + x^2 + y^2]/ Sqrt[1 + 2 x + x^2 + y^2]] Cos[(1/2) ArcTan[-((-1 + x^2 + y^2)/(1 + 2 x + x^2 + y^2)), -((2 y)/(1 + 2 x + x^2 + y^2))]] - 2 y Sqrt[Sqrt[1 - 2 x + x^2 + y^2]/Sqrt[1 + 2 x + x^2 + y^2]] Sin[(1/2) ArcTan[-((-1 + x^2 + y^2)/(1 + 2 x + x^2 + y^2)), -((2 y)/(1 + 2 x + x^2 + y^2))]])]]










Standard Form





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MathML Form







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





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





2001-10-29





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