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variants of this functions
WeierstrassSigma






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassSigma[n,z,{g2,g3}] > Primary definition





http://functions.wolfram.com/09.16.02.0001.01









  


  










Input Form





WeierstrassSigma[n, z, {Subscript[g, 2], Subscript[g, 3]}] == Exp[(-Subscript[\[Eta], n]) z] (WeierstrassSigma[z + Subscript[\[Omega], n], {Subscript[g, 2], Subscript[g, 3]}]/WeierstrassSigma[Subscript[\[Omega], n], {Subscript[g, 2], Subscript[g, 3]}]) /; Element[n, {1, 2, 3}] && {Subscript[\[Omega], 1], Subscript[\[Omega], 3]} == WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}] && Subscript[\[Omega], 2] == -Subscript[\[Omega], 1] - Subscript[\[Omega], 3] && Subscript[\[Eta], n] == WeierstrassZeta[Subscript[\[Omega], n], {Subscript[g, 2], Subscript[g, 3]}] && Element[n, {1, 2, 3}]










Standard Form





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MathML Form







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</mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> </mrow> <mstyle scriptlevel='0'> <mo> } </mo> </mstyle> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> &#951; </mi> <mi> n </mi> </msub> <mo> &#10869; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#969; </mi> <mi> n </mi> </msub> <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;\[Zeta]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[SubscriptBox[&quot;\[Omega]&quot;, &quot;n&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[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#963; </ci> <ci> n </ci> </apply> <ci> z </ci> <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> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <ci> n </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> WeierstrassSigma </ci> <apply> <plus /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <ci> n </ci> </apply> </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> <power /> <apply> <ci> WeierstrassSigma </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <ci> n </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> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </list> </apply> <apply> <eq /> <list> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </list> <list> <apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <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> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <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> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> <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> </apply> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> <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> </apply> </list> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <ci> n </ci> </apply> <apply> <ci> WeierstrassZeta </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <ci> n </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> <apply> <in /> <ci> n </ci> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </list> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassSigma", "[", RowBox[List["n_", ",", "z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SubscriptBox["\[Eta]", "n"]]], " ", "z"]]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List["z", "+", SubscriptBox["\[Omega]", "n"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["\[Omega]", "n"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]], "&&", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "\[Equal]", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]]]], "&&", RowBox[List[SubscriptBox["\[Omega]", "2"], "\[Equal]", RowBox[List[RowBox[List["-", SubscriptBox["\[Omega]", "1"]]], "-", SubscriptBox["\[Omega]", "3"]]]]], "&&", RowBox[List[SubscriptBox["\[Eta]", "n"], "\[Equal]", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]", "n"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "&&", RowBox[List["n", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]]]]]]]]]]










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





2001-10-29