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ArcCosh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCosh[z] > Transformations > Products, sums, and powers of the direct function > Linear combinations of the direct function





http://functions.wolfram.com/01.26.16.0161.01









  


  










Input Form





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





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