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variants of this functions
WeierstrassSigma




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.15.04.0007.01









  


  








Input Form





WeierstrassSigma[z t, {Subscript[g, 2], Subscript[g, 3]}] == t WeierstrassSigma[z, {Subscript[g, 2] t^4, Subscript[g, 3] t^6}] /; Element[t, Reals]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List["z", " ", "t"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List["t", " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["g", "2"], " ", SuperscriptBox["t", "4"]]], ",", RowBox[List[SubscriptBox["g", "3"], " ", SuperscriptBox["t", "6"]]]]], "}"]]]], "]"]]]]]], "/;", RowBox[List["t", "\[Element]", "Reals"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <mi> &#963; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mi> t </mi> </mrow> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Sigma]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[RowBox[List[&quot;z&quot;, &quot; &quot;, &quot;t&quot;]], Rule[Editable, True]], &quot;;&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]]]], &quot;,&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mi> t </mi> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#963; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ; </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <msup> <mi> t </mi> <mn> 4 </mn> </msup> </mrow> </mrow> <mo> , </mo> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <msup> <mi> t </mi> <mn> 6 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Sigma]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[&quot;z&quot;, Rule[Editable, True]], &quot;;&quot;, TagBox[RowBox[List[SubscriptBox[&quot;g&quot;, &quot;2&quot;], &quot; &quot;, SuperscriptBox[&quot;t&quot;, &quot;4&quot;]]], Rule[Editable, True]]]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;g&quot;, &quot;3&quot;], &quot; &quot;, SuperscriptBox[&quot;t&quot;, &quot;6&quot;]]], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> t </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> WeierstrassSigma </ci> <apply> <times /> <ci> z </ci> <ci> t </ci> </apply> <list> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> <apply> <times /> <ci> t </ci> <apply> <ci> WeierstrassSigma </ci> <ci> z </ci> <list> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> t </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> t </ci> <cn type='integer'> 6 </cn> </apply> </apply> </list> </apply> </apply> </apply> <apply> <in /> <ci> t </ci> <reals /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List["z_", " ", "t_"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["t", " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["gg", "2"], " ", SuperscriptBox["t", "4"]]], ",", RowBox[List[SubscriptBox["gg", "3"], " ", SuperscriptBox["t", "6"]]]]], "}"]]]], "]"]]]], "/;", RowBox[List["t", "\[Element]", "Reals"]]]]]]]]


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





2001-10-29