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ArcCosh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCosh[z] > Series representations > Generalized power series > Expansions on branch cuts > For the function itself > In the left half-plane





http://functions.wolfram.com/01.26.06.0046.01









  


  










Input Form





ArcCosh[z] == 2 Pi Floor[Arg[z - x]/(2 Pi)] Exp[(-((Pi I)/2)) Floor[Arg[z - x]/(2 Pi)]] + Pi I - (Sqrt[Pi]/2) Sqrt[x - 1] Sum[(((1 + x)^(1/2 - j) (1 - x)^(j - k))/ (j! (k - j)!)) Pochhammer[-(1/2), k - j] Hypergeometric2F1Regularized[ 1, 1, 3/2 - j, (1 + x)/2] (z - x)^k, {k, 0, Infinity}, {j, 0, k}] /; Element[x, Reals] && x < -1










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





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