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Mathematica Notation

Traditional Notation

Elliptic Functions > InverseJacobiNS[z,m] > General characteristics > Symmetries and periodicities > Quasi-reflection symmetry




Input Form

InverseJacobiNS[-z, m] == InverseJacobiNS[z, m] - (2/Sqrt[m]) InverseJacobiNS[1/z, 1/m]

Standard Form

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

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiNS", "[", RowBox[List[RowBox[List["-", "z_"]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["InverseJacobiNS", "[", RowBox[List["z", ",", "m"]], "]"]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["InverseJacobiNS", "[", RowBox[List[FractionBox["1", "z"], ",", FractionBox["1", "m"]]], "]"]]]], SqrtBox["m"]]]]]]]]

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