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ArcCosh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCosh[z] > Transformations > Related transformations > Linear combinations involving the direct function > Involving csch-1(z)





http://functions.wolfram.com/01.26.16.0233.01









  


  










Input Form





a ArcCosh[x] + b ArcCsch[y] == I Pi (1 - (-1)^(Floor[-(Arg[(Sqrt[1 + 1/y^2] + 1/y)^b (x + Sqrt[x - 1] Sqrt[x + 1])^ a + 1]/(2 Pi))] - Floor[-(Arg[(x + Sqrt[x - 1] Sqrt[x + 1])^a (Sqrt[1 + 1/y^2] + 1/y)^b]/ (2 Pi))])) + (-1)^(-Floor[-(Arg[(x + Sqrt[x - 1] Sqrt[x + 1])^a (Sqrt[1 + 1/y^2] + 1/y)^ b - 1]/(2 Pi))] + Floor[-(Arg[(Sqrt[1 + 1/y^2] + 1/y)^b (x + Sqrt[x - 1] Sqrt[x + 1])^a + 1]/(2 Pi))] + Floor[-(Arg[(x + Sqrt[x - 1] Sqrt[x + 1])^a (Sqrt[1 + 1/y^2] + 1/y)^b]/ Pi)] + Floor[Arg[(x + Sqrt[x - 1] Sqrt[x + 1])^a (Sqrt[1 + 1/y^2] + 1/y)^b]/Pi - (2 Arg[(x + Sqrt[x - 1] Sqrt[x + 1])^a (Sqrt[1 + 1/y^2] + 1/y)^b - 1])/ Pi]) ArcCosh[((1/2) ((Sqrt[1 + 1/y^2] + 1/y)^(2 b) (x + Sqrt[x - 1] Sqrt[x + 1])^(2 a) + 1))/ ((x + Sqrt[x - 1] Sqrt[x + 1])^a (Sqrt[1 + 1/y^2] + 1/y)^b)] - 2 I Pi (Floor[(-Arg[(x + Sqrt[x - 1] Sqrt[x + 1])^a] - Arg[(Sqrt[1 + 1/y^2] + 1/y)^b] + Pi)/(2 Pi)] + Floor[(Pi - Im[a Log[x + Sqrt[x - 1] Sqrt[x + 1]]])/(2 Pi)] + Floor[(Pi - Im[b Log[Sqrt[1 + 1/y^2] + 1/y]])/(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