|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/09.53.06.0005.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
EllipticNomeQ[m] \[Proportional] Exp[Pi^2/Log[(1 - m)/16]]
(1 + O[(m - 1)/Log[(1 - m)/16]^2]) /; (m -> 1)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticNomeQ", "[", "m", "]"]], "\[Proportional]", RowBox[List[RowBox[List["Exp", "[", FractionBox[SuperscriptBox["\[Pi]", "2"], RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", "m"]], "16"], "]"]]], "]"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", " ", FractionBox[RowBox[List["m", "-", "1"]], SuperscriptBox[RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", "m"]], "16"], "]"]], "2"]], "]"]]]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List["m", "\[Rule]", "1"]], ")"]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mn> 16 </mn> </mfrac> <mo> ) </mo> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mn> 16 </mn> </mfrac> <mo> ) </mo> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> EllipticNomeQ </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <exp /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 16 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <ln /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 16 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticNomeQ", "[", "m_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["\[Pi]", "2"], RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", "m"]], "16"], "]"]]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox[RowBox[List["m", "-", "1"]], SuperscriptBox[RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", "m"]], "16"], "]"]], "2"]], "]"]]]], ")"]]]], "/;", RowBox[List["(", RowBox[List["m", "\[Rule]", "1"]], ")"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|