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InverseJacobiNS




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.45.27.0006.01









  


  








Input Form





InverseJacobiNS[z, m] == EllipticK[m] + (I/Sqrt[m]) InverseJacobiDN[1/z, 1 - 1/m] /; z > -1 && m > 1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["InverseJacobiNS", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["EllipticK", "[", "m", "]"]], "+", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " "]], SqrtBox["m"]], RowBox[List["InverseJacobiDN", "[", RowBox[List[FractionBox["1", "z"], ",", RowBox[List["1", "-", FractionBox["1", "m"]]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["z", ">", RowBox[List["-", "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> ns </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> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mfrac> <mi> &#8520; </mi> <msqrt> <mi> m </mi> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> dn </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> &#10072; </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mn> 1 </mn> <mi> m </mi> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> z </mi> <mo> &gt; </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </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> InverseJacobiNS </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <plus /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <power /> <ci> m </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> InverseJacobiDN </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </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["InverseJacobiNS", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["EllipticK", "[", "m", "]"]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["InverseJacobiDN", "[", RowBox[List[FractionBox["1", "z"], ",", RowBox[List["1", "-", FractionBox["1", "m"]]]]], "]"]]]], SqrtBox["m"]]]], "/;", RowBox[List[RowBox[List["z", ">", RowBox[List["-", "1"]]]], "&&", RowBox[List["m", ">", "1"]]]]]]]]]]


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





2001-10-29