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InverseJacobiCN




Mathematica Notation

Traditional Notation









Elliptic Functions > InverseJacobiCN[z,m] > Representations through equivalent functions > With related functions > Involving ds-1





http://functions.wolfram.com/09.38.27.0007.01









  


  








Input Form





InverseJacobiCN[z, m] == (1/Sqrt[1 - m]) InverseJacobiDS[ 1/Sqrt[(z^2 - 1) (m - 1)], m/(m - 1)] /; z > 1 && m > 1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["InverseJacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["1", "-", "m"]]]], RowBox[List["InverseJacobiDS", "[", RowBox[List[FractionBox["1", RowBox[List[" ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], RowBox[List["(", RowBox[List["m", "-", "1"]], ")"]]]]]]]], ",", FractionBox["m", RowBox[List["m", "-", "1"]]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["z", ">", "1"]], "\[And]", RowBox[List["m", ">", "1"]]]]]]]]








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> <msup> <mi> cn </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> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> ds </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> </mfrac> <mo> &#10072; </mo> <mfrac> <mi> m </mi> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> z </mi> <mo> &gt; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> m </mi> <mo> &gt; </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> InverseJacobiCN </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> InverseJacobiDS </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> m </ci> <apply> <power /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <gt /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <gt /> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiCN", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["InverseJacobiDS", "[", RowBox[List[FractionBox["1", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["m", "-", "1"]], ")"]]]]]], ",", FractionBox["m", RowBox[List["m", "-", "1"]]]]], "]"]], SqrtBox[RowBox[List["1", "-", "m"]]]], "/;", RowBox[List[RowBox[List["z", ">", "1"]], "&&", RowBox[List["m", ">", "1"]]]]]]]]]]


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





2001-10-29