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http://functions.wolfram.com/01.27.06.0034.01
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ArcTanh[z] \[Proportional] z + z^3/3 + z^5/5 + O[z^7]
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Cell[BoxData[RowBox[List[RowBox[List["ArcTanh", "[", "z", "]"]], "\[Proportional]", RowBox[List["z", "+", FractionBox[SuperscriptBox["z", "3"], "3"], "+", FractionBox[SuperscriptBox["z", "5"], "5"], "+", RowBox[List["O", "[", SuperscriptBox["z", "7"], "]"]]]]]]]]
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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> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mn> 3 </mn> </mfrac> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mn> 5 </mn> </msup> <mn> 5 </mn> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <arctanh /> <ci> z </ci> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["z", "+", FractionBox[SuperscriptBox["z", "3"], "3"], "+", FractionBox[SuperscriptBox["z", "5"], "5"], "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "7"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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