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variants of this functions
EllipticTheta




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[4,z,q] > Differential equations > Partial differential equations





http://functions.wolfram.com/09.04.13.0003.01









  


  








Input Form





D[EllipticTheta[4, z, q], \[Tau]] == (-((Pi I)/4)) D[EllipticTheta[4, z, q], {z, 2}] /; q == E^(I Pi \[Tau])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "\[Tau]"], RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "z", ",", "q"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"]]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "2"]], "}"]]], RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "z", ",", "q"]], "]"]]]]]]]], "/;", RowBox[List["q", "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Tau]"]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> &#964; </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mn> 4 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> q </mi> <mo> &#10869; </mo> <msup> <mi> &#8519; </mi> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#964; </mi> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> &#964; </ci> </bvar> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <ci> z </ci> <ci> q </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <ci> z </ci> <ci> q </ci> </apply> </apply> </apply> </apply> <apply> <eq /> <ci> q </ci> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <pi /> <ci> &#964; </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["\[Tau]_"]]], RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "z_", ",", "q_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["-", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]], ")"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z", ",", "2"]], "}"]]]]], RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "z", ",", "q"]], "]"]]]]]], "/;", RowBox[List["q", "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Tau]"]]]]]]]]]]]


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





2001-10-29