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InverseJacobiCS




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.39.21.0001.01









  


  








Input Form





Integrate[InverseJacobiCS[z, m], z] == InverseJacobiCS[z, m] z + Log[JacobiDS[InverseJacobiCS[z, m], m] + JacobiNS[InverseJacobiCS[z, m], m]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["InverseJacobiCS", "[", RowBox[List["z", ",", "m"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["InverseJacobiCS", "[", RowBox[List["z", ",", "m"]], "]"]], " ", "z"]], "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["JacobiDS", "[", RowBox[List[RowBox[List["InverseJacobiCS", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]], "+", RowBox[List["JacobiNS", "[", RowBox[List[RowBox[List["InverseJacobiCS", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "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> <msup> <mi> cs </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <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> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> cs </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> ds </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mi> cs </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </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> ns </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mi> cs </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <ci> InverseJacobiCS </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <ci> InverseJacobiCS </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <ln /> <apply> <plus /> <apply> <ci> JacobiDS </ci> <apply> <ci> InverseJacobiCS </ci> <ci> z </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> <apply> <ci> JacobiNS </ci> <apply> <ci> InverseJacobiCS </ci> <ci> z </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["InverseJacobiCS", "[", RowBox[List["z_", ",", "m_"]], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["InverseJacobiCS", "[", RowBox[List["z", ",", "m"]], "]"]], " ", "z"]], "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["JacobiDS", "[", RowBox[List[RowBox[List["InverseJacobiCS", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]], "+", RowBox[List["JacobiNS", "[", RowBox[List[RowBox[List["InverseJacobiCS", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]]]], "]"]]]]]]]]


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





2001-10-29