html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 EllipticE

 http://functions.wolfram.com/08.04.21.0003.01

 Input Form

 Integrate[Sqrt[1 - m Sin[z]^2] EllipticE[z, m], z] == (1/2) EllipticE[z, m]^2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SqrtBox[RowBox[List["1", "-", RowBox[List["m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]]]], RowBox[List["EllipticE", "[", RowBox[List["z", ",", "m"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["EllipticE", "[", RowBox[List["z", ",", "m"]], "]"]], "2"]]]]]]]

 MathML Form

 E ( z m ) 1 - m sin 2 ( z ) z 1 2 E ( z m ) 2 z EllipticE z m 1 -1 m z 2 1 2 1 2 EllipticE z m 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SqrtBox[RowBox[List["1", "-", RowBox[List["m_", " ", SuperscriptBox[RowBox[List["Sin", "[", "z_", "]"]], "2"]]]]]], " ", RowBox[List["EllipticE", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["EllipticE", "[", RowBox[List["z", ",", "m"]], "]"]], "2"]]]]]]]

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

 2001-10-29