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InverseEllipticNomeQ






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseEllipticNomeQ[z] > Primary definition





http://functions.wolfram.com/09.52.02.0001.01









  


  










Input Form





InverseEllipticNomeQ[z] == 16 z Product[((1 + z^(2 k))/(1 + z^(2 k - 1)))^8, {k, 1, Infinity}] /; Abs[z] < 1










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "\[Equal]", RowBox[List["16", " ", "z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["2", " ", "k"]]]]], RowBox[List["1", "+", SuperscriptBox["z", RowBox[List[RowBox[List["2", " ", "k"]], "-", "1"]]]]]], ")"]], "8"]]]]]]], "/;", " ", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]










MathML Form







<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> &#10869; </mo> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <msup> <mi> z </mi> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mn> 8 </mn> </msup> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> z </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &lt; </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 8 </cn> </apply> </apply> </apply> </apply> <apply> <lt /> <apply> <abs /> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseEllipticNomeQ", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["16", " ", "z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["2", " ", "k"]]]]], RowBox[List["1", "+", SuperscriptBox["z", RowBox[List[RowBox[List["2", " ", "k"]], "-", "1"]]]]]], ")"]], "8"]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2001-10-29