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http://functions.wolfram.com/09.04.30.0001.01
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EllipticTheta[4, m Pi + (2 n + 1) ((Pi \[Tau])/2), q] == 0 /;
Element[{m, n}, Integers] && q == E^(I Pi \[Tau])
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", RowBox[List[RowBox[List["m", " ", "\[Pi]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", "n"]], "+", "1"]], ")"]], " ", FractionBox[RowBox[List["\[Pi]", " ", "\[Tau]"]], "2"]]]]], ",", "q"]], "]"]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["m", ",", "n"]], "}"]], "\[Element]", "Integers"]], "\[And]", RowBox[List["q", "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Tau]"]]]]]]]]]]]
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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> <msub> <mi> ϑ </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> τ </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> { </mo> <mrow> <mi> m </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> } </mo> </mrow> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> q </mi> <mo> ⩵ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> τ </mi> </mrow> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <ci> m </ci> <pi /> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <pi /> <ci> τ </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <ci> q </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <in /> <list> <ci> m </ci> <ci> n </ci> </list> <integers /> </apply> <apply> <eq /> <ci> q </ci> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <pi /> <ci> τ </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", RowBox[List[RowBox[List["m_", " ", "\[Pi]"]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "n_"]], "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[Tau]_"]], ")"]]]]]], ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["m", ",", "n"]], "}"]], "\[Element]", "Integers"]], "&&", RowBox[List["q", "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Tau]"]]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
