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InverseJacobiDN




Mathematica Notation

Traditional Notation









Elliptic Functions > InverseJacobiDN[z,m] > Transformations > Products, sums, and powers of the direct function





http://functions.wolfram.com/09.41.16.0002.01









  


  








Input Form





InverseJacobiDN[Subscript[z, 1], m] + InverseJacobiDN[Subscript[z, 2], m] == InverseJacobiDN[(m Subscript[z, 1] Subscript[z, 2] + Sqrt[(1 - Subscript[z, 1]^2) (Subscript[z, 1]^2 + m - 1) (1 - Subscript[z, 2]^2) (Subscript[z, 2]^2 + m - 1)])/ (m - (1 - Subscript[z, 1]^2) (1 - Subscript[z, 2]^2)), m]








Standard Form





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










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["InverseJacobiDN", "[", RowBox[List[SubscriptBox["z_", "1"], ",", "m_"]], "]"]], "+", RowBox[List["InverseJacobiDN", "[", RowBox[List[SubscriptBox["z_", "2"], ",", "m_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["InverseJacobiDN", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["m", " ", SubscriptBox["zz", "1"], " ", SubscriptBox["zz", "2"]]], "+", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["1", "-", SubsuperscriptBox["zz", "1", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List[SubsuperscriptBox["zz", "1", "2"], "+", "m", "-", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", SubsuperscriptBox["zz", "2", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List[SubsuperscriptBox["zz", "2", "2"], "+", "m", "-", "1"]], ")"]]]]]]], RowBox[List["m", "-", RowBox[List[RowBox[List["(", RowBox[List["1", "-", SubsuperscriptBox["zz", "1", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", SubsuperscriptBox["zz", "2", "2"]]], ")"]]]]]]], ",", "m"]], "]"]]]]]]


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





2001-10-29