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variants of this functions
EllipticTheta




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[2,z,q] > Differential equations > Partial differential equations





http://functions.wolfram.com/09.02.13.0002.01









  


  








Input Form





4 q D[EllipticTheta[2, z, q], q] + D[EllipticTheta[2, z, q], {z, 2}] == 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["4", "q", " ", RowBox[List[SubscriptBox["\[PartialD]", "q"], RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z", ",", "q"]], "]"]]]]]], "+", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "2"]], "}"]]], RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z", ",", "q"]], "]"]]]]]], "\[Equal]", "0"]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> q </mi> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> q </mi> </mrow> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mn> 2 </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> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> q </ci> <apply> <partialdiff /> <bvar> <ci> q </ci> </bvar> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <ci> z </ci> <ci> q </ci> </apply> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <ci> z </ci> <ci> q </ci> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["4", " ", "q_", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["q_"]]], RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z_", ",", "q_"]], "]"]]]]]], "+", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "2"]], "}"]]]]], RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z_", ",", "q_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", "0"]]]]


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





2001-10-29