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ArcSinh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.25.16.0201.01









  


  










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





2007-05-02