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http://functions.wolfram.com/01.27.06.0013.02
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ArcTanh[z] \[Proportional] (Pi z)/(2 Sqrt[-z^2]) + 1/z + 1/(3 z^3) +
1/(5 z^5) + \[Ellipsis] /; Abs[z] -> Infinity
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]], "+", FractionBox["1", "z"], "+", FractionBox["1", RowBox[List["3", " ", SuperscriptBox["z", "3"]]]], "+", FractionBox["1", RowBox[List["5", " ", SuperscriptBox["z", "5"]]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["Abs", "[", "z", "]"]]]], "\[Rule]", "\[Infinity]"]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <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> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> + </mo> <mfrac> <mn> 1 </mn> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 1 </mn> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mo> … </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> </mrow> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Rule </ci> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <arctanh /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <pi /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> … </ci> </apply> </apply> <apply> <abs /> <ci> z </ci> </apply> </apply> <infinity /> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]], "+", FractionBox["1", "z"], "+", FractionBox["1", RowBox[List["3", " ", SuperscriptBox["z", "3"]]]], "+", FractionBox["1", RowBox[List["5", " ", SuperscriptBox["z", "5"]]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["Abs", "[", "z", "]"]]]], "\[Rule]", "\[Infinity]"]]]] |
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Date Added to functions.wolfram.com (modification date)
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