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NevilleThetaD






Mathematica Notation

Traditional Notation









Elliptic Functions > NevilleThetaD[z,m] > Differential equations > Partial differential equations





http://functions.wolfram.com/09.10.13.0001.01









  


  










Input Form





EllipticK[m] D[NevilleThetaD[z, m], {z, 2}] + 2 z (EllipticE[m] + (m - 1) EllipticK[m]) D[NevilleThetaD[z, m], z] - 4 (m - 1) m EllipticK[m] D[NevilleThetaD[z, m], m] + (EllipticE[m] + m (EllipticK[m] - 1)) NevilleThetaD[z, m] == 0










Standard Form





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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> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> d </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mtext> </mtext> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> &#977; </mi> <mi> d </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mtext> </mtext> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> &#977; </mi> <mi> d </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> m </mi> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mi> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mi> d </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> NevilleThetaD </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <ci> EllipticE </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> NevilleThetaD </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <ci> m </ci> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <partialdiff /> <bvar> <ci> m </ci> </bvar> <apply> <ci> NevilleThetaD </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> <ci> m </ci> </apply> <apply> <ci> EllipticE </ci> <ci> m </ci> </apply> </apply> <apply> <ci> NevilleThetaD </ci> <ci> z </ci> <ci> m </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[RowBox[List["EllipticK", "[", "m_", "]"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "2"]], "}"]]]]], RowBox[List["NevilleThetaD", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]], "+", RowBox[List["2", " ", "z_", " ", RowBox[List["(", RowBox[List[RowBox[List["EllipticE", "[", "m_", "]"]], "+", RowBox[List[RowBox[List["(", RowBox[List["m_", "-", "1"]], ")"]], " ", RowBox[List["EllipticK", "[", "m_", "]"]]]]]], ")"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["NevilleThetaD", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List["m_", "-", "1"]], ")"]], " ", "m_", " ", RowBox[List["EllipticK", "[", "m_", "]"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["m_"]]], RowBox[List["NevilleThetaD", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["EllipticE", "[", "m_", "]"]], "+", RowBox[List["m_", " ", RowBox[List["(", RowBox[List[RowBox[List["EllipticK", "[", "m_", "]"]], "-", "1"]], ")"]]]]]], ")"]], " ", RowBox[List["NevilleThetaD", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", "0"]]]]










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





2001-10-29





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