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ArcSinh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.25.06.0036.01









  


  










Input Form





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