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ArcSinh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSinh[z] > Series representations > Generalized power series > Expansions at z==infinity > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.25.06.0070.01









  


  








Input Form





ArcSinh[z]^2 == Log[4 z^2]^2/4 + (Log[z^2]/(4 z^2)) HypergeometricPFQ[{3/2, 1, 1}, {2, 2}, -(1/z^2)] + (1/(2 z^2)) HypergeometricPFQ[{3/2, 1, 1, 1}, {2, 2, 2}, -(1/z^2)] - (1/(4 z^2)) Sum[((-1)^k Pochhammer[3/2, k] (PolyGamma[-(1/2) - k] - PolyGamma[k + 1]))/(z^(2 k) ((k + 1)^2 k!)), {k, 0, Infinity}] /; Abs[z] > 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