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InverseJacobiCS




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.39.27.0006.01









  


  








Input Form





InverseJacobiCS[z, m] == (I/Sqrt[m]) InverseJacobiDS[(I z)/Sqrt[m], (m - 1)/m] /; Element[z, Reals] && m < 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["InverseJacobiCS", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List[FractionBox["\[ImaginaryI]", SqrtBox["m"]], RowBox[List["InverseJacobiDS", "[", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["m"]], ",", FractionBox[RowBox[List["m", "-", "1"]], "m"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[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> cs </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> <mfrac> <mi> &#8520; </mi> <msqrt> <mi> m </mi> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> ds </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <msqrt> <mi> m </mi> </msqrt> </mfrac> <mo> &#10072; </mo> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> m </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> m </mi> <mo> &lt; </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> InverseJacobiCS </ci> <ci> z </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> InverseJacobiDS </ci> <apply> <times /> <imaginaryi /> <ci> z </ci> <apply> <power /> <apply> <power /> <ci> m </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> z </ci> <reals /> </apply> <apply> <lt /> <ci> m </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiCS", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["InverseJacobiDS", "[", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["m"]], ",", FractionBox[RowBox[List["m", "-", "1"]], "m"]]], "]"]]]], SqrtBox["m"]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["m", "<", "0"]]]]]]]]]]


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





2001-10-29