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InverseEllipticNomeQ




Mathematica Notation

Traditional Notation









Elliptic Functions > InverseEllipticNomeQ[z] > Differential equations > Ordinary nonlinear differential equations





http://functions.wolfram.com/09.52.13.0001.01









  


  








Input Form





Derivative[1][w][z] == (2 EllipticK[w[z]]^2 (w[z] - 1) w[z])/ (Pi z (EllipticK[1 - w[z]] (EllipticK[w[z]] - EllipticE[w[z]]) - EllipticE[1 - w[z]] EllipticK[w[z]])) /; w[z] == InverseEllipticNomeQ[z]








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> <msup> <mi> w </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mi> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> w </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <times /> <pi /> <ci> z </ci> <apply> <plus /> <apply> <times /> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> EllipticK </ci> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> EllipticE </ci> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> EllipticE </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <ci> EllipticK </ci> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29