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http://functions.wolfram.com/09.16.27.0006.01
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WeierstrassSigma[i, z, {Subscript[g, 2], Subscript[g, 3]}] ==
Exp[(Subscript[\[Eta], 1] z^2)/(2 Subscript[\[Omega], 1])]
(EllipticTheta[i + 1, (Pi z)/(2 Subscript[\[Omega], 1]), q]/
EllipticTheta[i + 1, 0, q]) /; Element[i, {1, 2, 3}]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List["i", ",", "z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Exp", "[", FractionBox[RowBox[List[SubscriptBox["\[Eta]", "1"], SuperscriptBox["z", "2"]]], RowBox[List["2", SubscriptBox["\[Omega]", "1"]]]], "]"]], " ", FractionBox[RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", SubscriptBox["\[Omega]", "1"]]]], ",", "q"]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]]]]]]], "/;", RowBox[List["i", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <msub> <mi> σ </mi> <mi> i </mi> </msub> <mo> ( </mo> <mrow> <mrow> <mi> u </mi> <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[SubscriptBox["\[Sigma]", "i"], "(", RowBox[List[RowBox[List[TagBox["u", Rule[Editable, True]], ";", TagBox[SubscriptBox["g", "2"], Rule[Editable, True]]]], ",", TagBox[SubscriptBox["g", "3"], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <msub> <mi> η </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mfrac> <mrow> <msub> <mi> ϑ </mi> <mrow> <mi> i </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> ϑ </mi> <mrow> <mi> i </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> i </mi> <mo> ∈ </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> WeierstrassSigma </ci> <ci> u </ci> <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 /> <apply> <exp /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> η </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <ci> EllipticTheta </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <pi /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> q </ci> </apply> <apply> <power /> <apply> <ci> EllipticTheta </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <in /> <ci> i </ci> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </list> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassSigma", "[", RowBox[List["i_", ",", "z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SubscriptBox["\[Eta]", "1"], " ", SuperscriptBox["z", "2"]]], RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]]]], " ", RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]]], ",", "q"]], "]"]]]], RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]]], "/;", RowBox[List["i", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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