Incomplete elliptic integral of the first kind: General characteristics (formula 08.05.04.0002)

EllipticF

$Mathematica Notation$

Elliptic Integrals

EllipticF[z,m]

General characteristics

Symmetries and periodicities

Parity

http://functions.wolfram.com/08.05.04.0002.01

Input Form

EllipticF[-z, m] == -EllipticF[z, m]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["-", "z"]], ",", "m"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> F </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mrow> <mi> F </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> EllipticF </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> EllipticF </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["-", "z_"]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]]

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

2001-10-29