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InverseJacobiDN




Mathematica Notation

Traditional Notation









Elliptic Functions > InverseJacobiDN[z,m] > Specific values > Specialized values > For fixed m





http://functions.wolfram.com/09.41.03.0004.01









  


  








Input Form





InverseJacobiDN[-1, m] == (2/Sqrt[m - 1]) EllipticK[1/(1 - m)] /; m > 1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["InverseJacobiDN", "[", RowBox[List[RowBox[List["-", "1"]], ",", "m"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["2", " "]], SqrtBox[RowBox[List["m", "-", "1"]]]], RowBox[List["EllipticK", "[", FractionBox["1", RowBox[List["1", "-", "m"]]], "]"]]]]]], "/;", 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> dn </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 2 </mn> <msqrt> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> m </mi> <mo> &gt; </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> InverseJacobiDN </ci> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <gt /> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiDN", "[", RowBox[List[RowBox[List["-", "1"]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["EllipticK", "[", FractionBox["1", RowBox[List["1", "-", "m"]]], "]"]]]], SqrtBox[RowBox[List["m", "-", "1"]]]], "/;", RowBox[List["m", ">", "1"]]]]]]]]


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





2001-10-29