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JacobiSN






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.36.13.0004.01









  


  










Input Form





4 m w[z, m]^4 Derivative[1, 0][w][z, m]^4 - w[z, m]^2 Derivative[1, 0][w][z, m]^2 (8 (-1 + m) m Derivative[1, 0][w][z, m] Derivative[1, 1][w][z, m] + Derivative[2, 0][w][z, m] (-8 (-1 + m) m Derivative[0, 1][w][z, m] + Derivative[2, 0][w][z, m])) + 2 (-1 + m) (Derivative[1, 0][w][z, m] Derivative[1, 1][w][z, m] - Derivative[0, 1][w][z, m] Derivative[2, 0][w][z, m]) (2 (-1 + m) m Derivative[1, 0][w][z, m] Derivative[1, 1][w][z, m] + Derivative[2, 0][w][z, m] (-2 (-1 + m) m Derivative[0, 1][w][z, m] + Derivative[2, 0][w][z, m])) == 0 /; w[z, m] == JacobiSN[z, m]










Standard Form





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MathML Form







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</mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </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> <mrow> <msup> <mi> w </mi> <semantics> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;0&quot;]], &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> w </mi> <semantics> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;1&quot;]], &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <msup> <mi> w </mi> <semantics> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;2&quot;, &quot;,&quot;, &quot;0&quot;]], &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> w </mi> <semantics> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;2&quot;, &quot;,&quot;, &quot;0&quot;]], &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 2 </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> <mrow> <msup> <mi> w </mi> <semantics> <mrow> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;0&quot;, &quot;,&quot;, &quot;1&quot;]], &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> sn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> m </ci> <apply> <power /> <apply> <ci> w </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> w </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <ci> m </ci> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 2 </cn> <cn type='integer'> 0 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> <apply> <plus /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 2 </cn> <cn type='integer'> 0 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <ci> m </ci> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 1 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 1 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 2 </cn> <cn type='integer'> 0 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <ci> m </ci> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 2 </cn> <cn type='integer'> 0 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> <apply> <plus /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 2 </cn> <cn type='integer'> 0 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <ci> m </ci> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 1 </cn> </list> <ci> w </ci> </apply> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <ci> JacobiSN </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





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