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JacobiDS




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiDS[z,m] > Integration > Indefinite integration > Involving only one direct function





http://functions.wolfram.com/09.30.21.0001.01









  


  








Input Form





Integrate[JacobiDS[z, m], z] == Log[(1 - JacobiCN[z, m])/JacobiSN[z, m]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["JacobiDS", "[", RowBox[List["z", ",", "m"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", RowBox[List["JacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]]]], RowBox[List["JacobiSN", "[", RowBox[List["z", ",", "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> <mo> &#8747; </mo> <mrow> <mrow> <mi> ds </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <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> <mi> sn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <ci> JacobiDS </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <ln /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> JacobiCN </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <power /> <apply> <ci> JacobiSN </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["JacobiDS", "[", RowBox[List["z_", ",", "m_"]], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", RowBox[List["JacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]]]], RowBox[List["JacobiSN", "[", RowBox[List["z", ",", "m"]], "]"]]], "]"]]]]]]


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





2001-10-29