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ArcCoth




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCoth[z] > Series representations > Generalized power series > Expansions at z==-1 > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.28.06.0060.01









  


  








Input Form





ArcCoth[z]^2 == Subscript[F, Infinity][z] /; Subscript[F, n][z] == (1/4) Log[(-z - 1)/2]^2 + ((z + 1)/4) Log[(-z - 1)/2] Sum[(z + 1)^k/(2^k (k + 1)), {k, 0, n}] + ((z + 1)^2/16) Sum[(z + 1)^k/(2^k (k + 1)), {k, 0, n}]^2 == (((2^(-n - 3) (1 + z)^(2 + n))/(n + 2)) Hypergeometric2F1[1, 2 + n, 3 + n, (1 + z)/2] - (1/2) Log[-z - 1] + (1/2) Log[1 - z])^2 && Element[n, Integers] && n >= 0








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