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InverseJacobiCN




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.38.27.0006.01









  


  








Input Form





InverseJacobiCN[z, m] == InverseJacobiDN[Sqrt[1 - m + m z^2], m] /; (0 < z < 1 && m > 1) || (-1 < z < 0 && m < 0)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["InverseJacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List["InverseJacobiDN", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "m", "+", RowBox[List["m", " ", SuperscriptBox["z", "2"]]]]]], ",", "m"]], "]"]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["0", "<", "z", "<", "1"]], "\[And]", RowBox[List["m", ">", "1"]]]], ")"]], "\[Or]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "0"]], "\[And]", RowBox[List["m", "<", "0"]]]], ")"]]]]]]]]








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> <msup> <mi> dn </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <msqrt> <mrow> <mrow> <mi> m </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mn> 0 </mn> <mo> &lt; </mo> <mi> z </mi> <mo> &lt; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> m </mi> <mo> &gt; </mo> <mn> 1 </mn> </mrow> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> &lt; </mo> <mi> z </mi> <mo> &lt; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> m </mi> <mo> &lt; </mo> <mn> 0 </mn> </mrow> </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> <ci> InverseJacobiDN </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> m </ci> </apply> </apply> <apply> <or /> <apply> <and /> <apply> <lt /> <cn type='integer'> 0 </cn> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <gt /> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <and /> <apply> <lt /> <cn type='integer'> -1 </cn> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <lt /> <ci> m </ci> <cn type='integer'> 0 </cn> </apply> </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[RowBox[List["InverseJacobiDN", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", "m", "+", RowBox[List["m", " ", SuperscriptBox["z", "2"]]]]]], ",", "m"]], "]"]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["0", "<", "z", "<", "1"]], "&&", RowBox[List["m", ">", "1"]]]], ")"]], "||", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "0"]], "&&", RowBox[List["m", "<", "0"]]]], ")"]]]]]]]]]]


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





2001-10-29