Complete elliptic integral of the first kind: Representations through more general functions (formula 08.02.26.0128)

EllipticK

$Mathematica Notation$

Elliptic Integrals

EllipticK[z]

Representations through more general functions

Through other functions

Involving incomplete elliptic integrals

http://functions.wolfram.com/08.02.26.0128.01

Input Form

EllipticK[z] == EllipticPi[0, Pi/2, z]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["EllipticK", "[", "z", "]"]], "\[Equal]", RowBox[List["EllipticPi", "[", RowBox[List["0", ",", FractionBox["\[Pi]", "2"], ",", "z"]], "]"]]]]]]

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> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> Π </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> ; </mo> <mrow> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> <mo> ❘ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> EllipticK </ci> <ci> z </ci> </apply> <apply> <ci> EllipticPi </ci> <cn type='integer'> 0 </cn> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> z </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticK", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["EllipticPi", "[", RowBox[List["0", ",", FractionBox["\[Pi]", "2"], ",", "z"]], "]"]]]]]]

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

2001-10-29