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ArcCsch




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsch[z] > Series representations > Generalized power series > Expansions at z==0 > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.29.06.0043.01









  


  








Input Form





ArcCsch[z]^2 == (1/4) Log[4/z^2]^2 + (z^2/4) Log[1/z^2] HypergeometricPFQ[{3/2, 1, 1}, {2, 2}, -z^2] + (z^2/2) HypergeometricPFQ[{3/2, 1, 1, 1}, {2, 2, 2}, -z^2] - (z^2/4) Sum[((-1)^k Pochhammer[3/2, k] ((PolyGamma[-(1/2) - k] - PolyGamma[k + 1])/((k + 1)^2 k!)))/z^(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