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http://functions.wolfram.com/09.17.27.0004.01
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WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] ==
(Subscript[\[Eta], 1] z)/Subscript[\[Omega], 1] +
(Pi/(2 Subscript[\[Omega], 1]))
(EllipticThetaPrime[1, (Pi z)/(2 Subscript[\[Omega], 1]), q]/
EllipticTheta[1, (Pi z)/(2 Subscript[\[Omega], 1]), q])
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Cell[BoxData[RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SubscriptBox["\[Eta]", "1"], " ", "z"]], SubscriptBox["\[Omega]", "1"]], "+", RowBox[List[FractionBox["\[Pi]", RowBox[List["2", SubscriptBox["\[Omega]", "1"]]]], " ", FractionBox[RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", SubscriptBox["\[Omega]", "1"]]]], ",", "q"]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", SubscriptBox["\[Omega]", "1"]]]], ",", "q"]], "]"]]]]]]]]]]]
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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> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </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["\[Zeta]", "(", RowBox[List[RowBox[List[TagBox["z", Rule[Editable, True]], ";", TagBox[SubscriptBox["g", "2"], Rule[Editable, True]]]], ",", TagBox[SubscriptBox["g", "3"], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <mi> z </mi> <mo> ⁢ </mo> <msub> <mi> η </mi> <mn> 1 </mn> </msub> </mrow> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi>  </mi> <mo> ⁢ </mo> <mrow> <msubsup> <mi> ϑ </mi> <mn> 1 </mn> <mo> ′ </mo> </msubsup> <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> <mtext> </mtext> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </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> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> WeierstrassZeta </ci> <ci> z </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> <plus /> <apply> <times /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> η </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci>  </ci> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <apply> <ci> Subscript </ci> <ci> ϑ </ci> <cn type='integer'> 1 </cn> </apply> </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> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <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> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassZeta", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SubscriptBox["\[Eta]", "1"], " ", "z"]], SubscriptBox["\[Omega]", "1"]], "+", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]]], ",", "q"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]], ")"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]]], ",", "q"]], "]"]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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