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ArcTanh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Series representations > Generalized power series > Expansions at z==infinity > For the function itself





http://functions.wolfram.com/01.27.06.0060.01









  


  










Input Form





ArcTanh[z] == Subscript[F, Infinity][z] /; Subscript[F, n][z] == (Pi z)/(2 Sqrt[-z^2]) + Sum[z^(-2 k - 1)/(2 k + 1), {k, 0, n}] == ArcTanh[z] - (z^(-3 - 2 n)/(3 + 2 n)) Hypergeometric2F1[1, 3/2 + n, 5/2 + n, 1/z^2] && Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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</mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mfrac> <msup> <mi> z </mi> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> </msup> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mrow> <mi> n </mi> <mo> + </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mrow> <mi> n </mi> <mo> + </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; 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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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