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InverseJacobiCD




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.37.27.0004.01









  


  








Input Form





InverseJacobiCD[z, m] == InverseJacobiDC[1/z, m] /; (z < 0 && m < 0) || (z < 1 && m < 1)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["InverseJacobiCD", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List["InverseJacobiDC", "[", RowBox[List[FractionBox["1", "z"], ",", "m"]], "]"]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["z", "<", "0"]], "\[And]", RowBox[List["m", "<", "0"]]]], ")"]], "\[Or]", RowBox[List["(", RowBox[List[RowBox[List["z", "<", "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> cd </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> <msup> <mi> dc </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> z </mi> <mo> &lt; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> m </mi> <mo> &lt; </mo> <mn> 0 </mn> </mrow> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mi> z </mi> <mo> &lt; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> m </mi> <mo> &lt; </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> InverseJacobiCD </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <ci> InverseJacobiDC </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> m </ci> </apply> </apply> <apply> <or /> <apply> <and /> <apply> <lt /> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <lt /> <ci> m </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <and /> <apply> <lt /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <lt /> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiCD", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["InverseJacobiDC", "[", RowBox[List[FractionBox["1", "z"], ",", "m"]], "]"]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["z", "<", "0"]], "&&", RowBox[List["m", "<", "0"]]]], ")"]], "||", RowBox[List["(", RowBox[List[RowBox[List["z", "<", "1"]], "&&", RowBox[List["m", "<", "1"]]]], ")"]]]]]]]]]]


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





2001-10-29