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JacobiDN




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiDN[z,m] > Representations through equivalent functions > With related functions > Involving theta functions





http://functions.wolfram.com/09.29.27.0030.01









  


  








Input Form





JacobiZeta[JacobiAmplitude[u, m], m] + JacobiZeta[JacobiAmplitude[v, m], m] - JacobiZeta[JacobiAmplitude[u + v, m], m] == m JacobiSN[v, m] JacobiSN[u, m] JacobiSN[u + v, m]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List["u", ",", "m"]], "]"]], ",", "m"]], "]"]], "+", RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List["v", ",", "m"]], "]"]], ",", "m"]], "]"]], "-", RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List[RowBox[List["u", "+", "v"]], ",", "m"]], "]"]], ",", "m"]], "]"]]]], "\[Equal]", RowBox[List["m", " ", RowBox[List["JacobiSN", "[", RowBox[List["v", ",", "m"]], "]"]], " ", RowBox[List["JacobiSN", "[", RowBox[List["u", ",", "m"]], "]"]], " ", RowBox[List["JacobiSN", "[", RowBox[List[RowBox[List["u", "+", "v"]], ",", "m"]], "]"]]]]]]]]








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> <mi> &#918; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> am </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> u </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> &#918; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> am </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> v </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> &#918; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> am </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> u </mi> <mo> + </mo> <mi> v </mi> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mrow> <mi> sn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> v </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> u </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> u </mi> <mo> + </mo> <mi> v </mi> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <ci> JacobiZeta </ci> <apply> <ci> JacobiAmplitude </ci> <ci> u </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> <apply> <ci> JacobiZeta </ci> <apply> <ci> JacobiAmplitude </ci> <ci> v </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> JacobiZeta </ci> <apply> <ci> JacobiAmplitude </ci> <apply> <plus /> <ci> u </ci> <ci> v </ci> </apply> <ci> m </ci> </apply> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <ci> m </ci> <apply> <ci> JacobiSN </ci> <ci> v </ci> <ci> m </ci> </apply> <apply> <ci> JacobiSN </ci> <ci> u </ci> <ci> m </ci> </apply> <apply> <ci> JacobiSN </ci> <apply> <plus /> <ci> u </ci> <ci> v </ci> </apply> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List["u_", ",", "m_"]], "]"]], ",", "m_"]], "]"]], "+", RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List["v_", ",", "m_"]], "]"]], ",", "m_"]], "]"]], "-", RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List[RowBox[List["u_", "+", "v_"]], ",", "m_"]], "]"]], ",", "m_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["m", " ", RowBox[List["JacobiSN", "[", RowBox[List["v", ",", "m"]], "]"]], " ", RowBox[List["JacobiSN", "[", RowBox[List["u", ",", "m"]], "]"]], " ", RowBox[List["JacobiSN", "[", RowBox[List[RowBox[List["u", "+", "v"]], ",", "m"]], "]"]]]]]]]]


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





2001-10-29