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ArcSinh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSinh[z] > Transformations > Related transformations > Sums involving the direct function > Involving cosh-1(z)





http://functions.wolfram.com/01.25.16.0167.01









  


  










Input Form





ArcSinh[x] + ArcCosh[y] == ArcSinh[ I (-1)^Floor[1/2 - Arg[I x y + I Sqrt[1 + x^2] Sqrt[-1 + y] Sqrt[1 + y]]/ Pi] (Sqrt[1 + x^2] y + x Sqrt[-1 + y] Sqrt[1 + y])] - (1/2) Pi I ((-(1/2)) (1 + (-1)^(-Floor[-(Arg[1 - y]/(2 Pi))])) ((-1)^Floor[1/2 - Arg[(-I) x y + Sqrt[1 + x^2] Sqrt[1 - y^2]]/Pi] + 2 (-1 + (-1)^Floor[1/2 - Arg[(-I) x y + Sqrt[1 + x^2] Sqrt[1 - y^2]]/ Pi]) Floor[(Arg[-x + Sqrt[1 + x^2]] + Arg[I y + Sqrt[1 - y^2]])/ (2 Pi)] + 2 (1 + (-1)^Floor[1/2 - Arg[(-I) x y + Sqrt[1 + x^2] Sqrt[1 - y^2]]/ Pi]) Floor[1/2 - (Arg[-x + Sqrt[1 + x^2]] + Arg[I y + Sqrt[1 - y^2]])/(2 Pi)]) + (1/2) (1 - (-1)^(-Floor[-(Arg[1 - y]/(2 Pi))])) ((-1)^Floor[1/2 - Arg[I x y + Sqrt[1 + x^2] Sqrt[1 - y^2]]/Pi] + 2 (-1 + (-1)^Floor[1/2 - Arg[I x y + Sqrt[1 + x^2] Sqrt[1 - y^2]]/Pi]) Floor[(Arg[x + Sqrt[1 + x^2]] + Arg[I y + Sqrt[1 - y^2]])/(2 Pi)] + 2 (1 + (-1)^Floor[1/2 - Arg[I x y + Sqrt[1 + x^2] Sqrt[1 - y^2]]/Pi]) Floor[1/2 - (Arg[x + Sqrt[1 + x^2]] + Arg[I y + Sqrt[1 - y^2]])/ (2 Pi)]))










Standard Form





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MathML Form







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</msqrt> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> <mo> + </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> </mrow> <mo> &#8971; </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mrow> <mo> &#8970; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> y </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> </mrow> <mo> 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Rule Form





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





2007-05-02