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   http://functions.wolfram.com/09.52.06.0008.01
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    InverseEllipticNomeQ[z] \[Proportional] 1 - 16 E^(Pi^2/Log[z]) + 
   O[E^((2 Pi^2)/Log[z])] /; Abs[z] < 1 && (z -> 1) 
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   Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "\[Proportional]", RowBox[List["1", "-", RowBox[List["16", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["\[Pi]", "2"], RowBox[List["Log", "[", "z", "]"]]]]]], "+", RowBox[List["O", "[", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[Pi]", "2"]]], RowBox[List["Log", "[", "z", "]"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]], "\[And]", RowBox[List["(", RowBox[List["z", "\[Rule]", "1"]], ")"]]]]]]]] 
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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>  <msup>  <semantics>  <mi> q </mi>  <annotation-xml encoding='MathML-Content'>  <ci> EllipticNomeQ </ci>  </annotation-xml>  </semantics>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msup>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mo> ∝ </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mrow>  <mn> 16 </mn>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mfrac>  <msup>  <mi> π </mi>  <mn> 2 </mn>  </msup>  <mrow>  <mi> log </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mfrac>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mi> O </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <msup>  <mi> ⅇ </mi>  <mfrac>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msup>  <mi> π </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mrow>  <mi> log </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mfrac>  </msup>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> /; </mo>  <mrow>  <mrow>  <mrow>  <semantics>  <mo> ❘ </mo>  <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation>  </semantics>  <mi> z </mi>  <semantics>  <mo> ❘ </mo>  <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation>  </semantics>  </mrow>  <mo> < </mo>  <mn> 1 </mn>  </mrow>  <mo> ∧ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <semantics>  <mo> → </mo>  <annotation encoding='Mathematica'> "\[Rule]" </annotation>  </semantics>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <ci> Condition </ci>  <apply>  <ci> Proportional </ci>  <apply>  <ci> InverseEllipticNomeQ </ci>  <ci> z </ci>  </apply>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 16 </cn>  <apply>  <power />  <exponentiale />  <apply>  <times />  <apply>  <power />  <pi />  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <apply>  <ln />  <ci> z </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <ci> O </ci>  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <pi />  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <apply>  <ln />  <ci> z </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <and />  <apply>  <lt />  <apply>  <abs />  <ci> z </ci>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <ci> Rule </ci>  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseEllipticNomeQ", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["1", "-", RowBox[List["16", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["\[Pi]", "2"], RowBox[List["Log", "[", "z", "]"]]]]]], "+", SuperscriptBox[RowBox[List["O", "[", "\[ExponentialE]", "]"]], FractionBox[RowBox[List["2", " ", SuperscriptBox["\[Pi]", "2"]]], RowBox[List["Log", "[", "z", "]"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]], "&&", RowBox[List["(", RowBox[List["z", "\[Rule]", "1"]], ")"]]]]]]]]]]  |  
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   Date Added to functions.wolfram.com (modification date)
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