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ArcSinh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSinh[z] > Transformations > Products, sums, and powers of the direct function > Sums of the direct function





http://functions.wolfram.com/01.25.16.0136.01









  


  










Input Form





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










Standard Form





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MathML Form







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Rule Form





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





2007-05-02