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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/08.05.16.0006.01









  


  








Input Form





EllipticF[ArcSin[Sqrt[m] Sin[z]], 1/m] == Sqrt[m] EllipticF[z, m] /; -(Pi/2) < z < Pi/2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["ArcSin", "[", RowBox[List[SqrtBox["m"], RowBox[List["Sin", "[", "z", "]"]]]], "]"]], ",", FractionBox["1", "m"]]], "]"]], "\[Equal]", RowBox[List[SqrtBox["m"], RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", "z", "<", FractionBox["\[Pi]", "2"]]]]]]]








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> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <msqrt> <mi> m </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10072; </mo> <mfrac> <mn> 1 </mn> <mi> m </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msqrt> <mi> m </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> F </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> &lt; </mo> <mi> z </mi> <mo> &lt; </mo> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> EllipticF </ci> <apply> <arcsin /> <apply> <times /> <apply> <power /> <ci> m </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sin /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> m </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> EllipticF </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <lt /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> z </ci> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["ArcSin", "[", RowBox[List[SqrtBox["m_"], " ", RowBox[List["Sin", "[", "z_", "]"]]]], "]"]], ",", FractionBox["1", "m_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SqrtBox["m"], " ", RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", "z", "<", FractionBox["\[Pi]", "2"]]]]]]]]]


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





2001-10-29