InverseJacobiCN[0, m] == EllipticK[m] /; Element[m, Reals] && m < 1

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["InverseJacobiCN", "[", RowBox[List["0", ",", "m"]], "]"]], "\[Equal]", RowBox[List["EllipticK", "[", "m", "]"]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["m", ",", "Reals"]], "]"]], "\[And]", " ", RowBox[List["m", "<", "1"]]]]]]]]

<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> cn </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> m </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> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> InverseJacobiCN </ci> <cn type='integer'> 0 </cn> <ci> m </ci> </apply> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> </apply> <apply> <and /> <apply> <in /> <ci> m </ci> <reals /> </apply> <apply> <lt /> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiCN", "[", RowBox[List["0", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["EllipticK", "[", "m", "]"]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Reals"]], "&&", RowBox[List["m", "<", "1"]]]]]]]]]]

2001-10-29