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EllipticF




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticF[z,m] > Transformations > Transformations and argument simplifications > Argument involving inverse trigonometric functions





http://functions.wolfram.com/08.05.16.0004.01









  


  








Input Form





EllipticF[ArcCos[z], m] == InverseJacobiCN[z, m] /; -1 < z < 1 && Element[m, Reals]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["ArcCos", "[", "z", "]"]], ",", "m"]], "]"]], "\[Equal]", RowBox[List["InverseJacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "1"]], "\[And]", RowBox[List["m", "\[Element]", "Reals"]]]]]]]]








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> <mi> F </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mi> cn </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> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> &lt; </mo> <mi> z </mi> <mo> &lt; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> m </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> EllipticF </ci> <apply> <arccos /> <ci> z </ci> </apply> <ci> m </ci> </apply> <apply> <ci> InverseJacobiCN </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <and /> <apply> <lt /> <cn type='integer'> -1 </cn> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <in /> <ci> m </ci> <reals /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["ArcCos", "[", "z_", "]"]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["InverseJacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]], "/;", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "1"]], "&&", RowBox[List["m", "\[Element]", "Reals"]]]]]]]]]]


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





2001-10-29