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ArcCosh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCosh[z] > Representations through more general functions > Through Meijer G > Generalized cases for the direct function itself





http://functions.wolfram.com/01.26.26.0033.01









  


  








Input Form





ArcCosh[z] - (Pi Sqrt[-1 + z])/(2 Sqrt[1 - z]) + (Sqrt[-1 + z] z Log[-4 z^2])/ (2 Sqrt[1 - z] Sqrt[-z^2]) - ((Sqrt[-1 + z] z)/(2 Sqrt[1 - z] Sqrt[-z^2])) Sum[Pochhammer[1/2, k]/(z^(2 k) (k k!)), {k, 1, n}] == (((-1)^(-1 + n) Sqrt[-1 + z] z)/(2 Sqrt[Pi] Sqrt[1 - z] Sqrt[-z^2])) MeijerG[{{1/2, 1, 1 + n}, {}}, {{1 + n}, {0, 0}}, -(I/z), 1/2] /; Element[n, Integers] && n >= 0 && !IntervalMemberQ[Interval[{-1, 1}], z]








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)





2003-08-21