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WeierstrassZeta






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassZeta[z,{g2,g3}] > General characteristics > Symmetries and periodicities > Homogeneity





http://functions.wolfram.com/09.17.04.0007.01









  


  










Input Form





WeierstrassZeta[\[Lambda] z, WeierstrassInvariants[ \[Lambda] WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}]]] == WeierstrassZeta[\[Lambda] z, {Subscript[g, 2]/\[Lambda]^4, Subscript[g, 3]/\[Lambda]^6}]










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> &#955; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ; </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> &#955; </mi> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mi> &#955; </mi> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> &#955; </mi> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mi> &#955; </mi> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[RowBox[List[&quot;\[Lambda]&quot;, &quot; &quot;, &quot;z&quot;]], Rule[Editable, True]], &quot;;&quot;, TagBox[RowBox[List[SubscriptBox[&quot;g&quot;, &quot;2&quot;], &quot;(&quot;, RowBox[List[RowBox[List[&quot;\[Lambda]&quot;, &quot; &quot;, SubscriptBox[&quot;\[Omega]&quot;, &quot;1&quot;]]], &quot;,&quot;, RowBox[List[&quot;\[Lambda]&quot;, &quot; &quot;, SubscriptBox[&quot;\[Omega]&quot;, &quot;3&quot;]]]]], &quot;)&quot;]], Rule[Editable, True]]]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;g&quot;, &quot;3&quot;], &quot;(&quot;, RowBox[List[RowBox[List[&quot;\[Lambda]&quot;, &quot; &quot;, SubscriptBox[&quot;\[Omega]&quot;, &quot;1&quot;]]], &quot;,&quot;, RowBox[List[&quot;\[Lambda]&quot;, &quot; &quot;, SubscriptBox[&quot;\[Omega]&quot;, &quot;3&quot;]]]]], &quot;)&quot;]], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> &#10869; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> &#955; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ; </mo> <mfrac> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <msup> <mi> &#955; </mi> <mn> 4 </mn> </msup> </mfrac> </mrow> <mo> , </mo> <mfrac> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <msup> <mi> &#955; </mi> <mn> 6 </mn> </msup> </mfrac> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[RowBox[List[&quot;\[Lambda]&quot;, &quot; &quot;, &quot;z&quot;]], Rule[Editable, True]], &quot;;&quot;, TagBox[FractionBox[RowBox[List[SubscriptBox[&quot;g&quot;, &quot;2&quot;], &quot;(&quot;, RowBox[List[SubscriptBox[&quot;\[Omega]&quot;, &quot;1&quot;], &quot;,&quot;, SubscriptBox[&quot;\[Omega]&quot;, &quot;3&quot;]]], &quot;)&quot;]], SuperscriptBox[&quot;\[Lambda]&quot;, &quot;4&quot;]], Rule[Editable, True]]]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[SubscriptBox[&quot;g&quot;, &quot;3&quot;], &quot;(&quot;, RowBox[List[SubscriptBox[&quot;\[Omega]&quot;, &quot;1&quot;], &quot;,&quot;, SubscriptBox[&quot;\[Omega]&quot;, &quot;3&quot;]]], &quot;)&quot;]], SuperscriptBox[&quot;\[Lambda]&quot;, &quot;6&quot;]], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> WeierstrassZeta </ci> <apply> <times /> <ci> &#955; </ci> <ci> z </ci> </apply> <list> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <ci> &#955; </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <ci> &#955; </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <ci> &#955; </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <ci> &#955; </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </list> </apply> <apply> <ci> WeierstrassZeta </ci> <apply> <times /> <ci> &#955; </ci> <ci> z </ci> </apply> <list> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 6 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </list> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["\[Lambda]_", " ", "z_"]], ",", RowBox[List["WeierstrassInvariants", "[", RowBox[List["\[Lambda]_", " ", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]], "]"]]]], "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["\[Lambda]", " ", "z"]], ",", RowBox[List["{", RowBox[List[FractionBox[SubscriptBox["gg", "2"], SuperscriptBox["\[Lambda]", "4"]], ",", FractionBox[SubscriptBox["gg", "3"], SuperscriptBox["\[Lambda]", "6"]]]], "}"]]]], "]"]]]]]]










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





2001-10-29