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JacobiAmplitude






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiAmplitude[z,m] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/09.24.20.0010.01









  


  










Input Form





D[JacobiAmplitude[z, m], {z, n}] == JacobiAmplitude[z, m] KroneckerDelta[n] + JacobiDN[z, m] KroneckerDelta[n - 1] - m Sum[Binomial[n - 2, j] D[JacobiSN[z, m], {z, j}] D[JacobiCN[z, m], {z, n - 2 - j}], {j, 0, n - 2}] /; Element[n, Integers] && n >= 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> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mi> n </mi> </msup> <mrow> <mi> am </mi> <mo> &#8289; </mo> <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> <mi> n </mi> </msup> </mrow> </mfrac> <mo> &#63449; </mo> <mrow> <mrow> <mrow> <mi> dn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> + </mo> <mrow> <mrow> <mi> am </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mi> n </mi> </msub> </mrow> <mo> - </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </munderover> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mi> n </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mi> j </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[&quot;n&quot;, &quot;-&quot;, &quot;2&quot;]], Identity, Rule[Editable, True]]], List[TagBox[&quot;j&quot;, Identity, Rule[Editable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mi> j </mi> </msup> <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> <mo> &#8706; </mo> <msup> <mi> z </mi> <mi> j </mi> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mrow> <mrow> <mo> - </mo> <mi> j </mi> </mrow> <mo> + </mo> <mi> n </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mrow> <mi> cn </mi> <mo> &#8289; </mo> <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> <mrow> <mrow> <mo> - </mo> <mi> j </mi> </mrow> <mo> + </mo> <mi> n </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <ci> n </ci> </degree> </bvar> <apply> <ci> JacobiAmplitude </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> JacobiDN </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <ci> JacobiAmplitude </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <ci> KroneckerDelta </ci> <ci> n </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> m </ci> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> n </ci> <cn type='integer'> -2 </cn> </apply> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -2 </cn> </apply> <ci> j </ci> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <ci> j </ci> </degree> </bvar> <apply> <ci> JacobiSN </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <ci> n </ci> <cn type='integer'> -2 </cn> </apply> </degree> </bvar> <apply> <ci> JacobiCN </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </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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