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http://functions.wolfram.com/09.21.03.0002.01
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WeierstrassZetaHalfPeriodValues[{1, 0}] == {Pi/(4 Subscript[\[Omega], 1]),
(Pi/(4 Subscript[\[Omega], 1])) (1 - I),
-((Pi I)/(4 Subscript[\[Omega], 1]))} /;
WeierstrassInvariants[{Subscript[\[Omega], 1], Subscript[\[Omega], 3]}] ==
{1, 0}
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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> <mrow> <mo> { </mo> <mrow> <mrow> <msub> <mi> η </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msub> <mi> η </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msub> <mi> η </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> } </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mfrac> <mi> π </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> , </mo> <mrow> <mfrac> <mi> π </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> { </mo> <mrow> <semantics> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox["g", "2"], Rule[Editable, True]] </annotation> </semantics> <mo> , </mo> <semantics> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox["g", "3"], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> } </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <list> <apply> <apply> <ci> Subscript </ci> <ci> η </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> </apply> <apply> <apply> <ci> Subscript </ci> <ci> η </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> </apply> <apply> <apply> <ci> Subscript </ci> <ci> η </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> </apply> </list> <list> <apply> <times /> <pi /> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <pi /> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='complex-cartesian'> 1 <sep /> -1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> </apply> <apply> <eq /> <list> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </list> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> </list> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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