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 EllipticPi

 http://functions.wolfram.com/08.03.20.0003.01

 Input Form

 D[EllipticPi[n, m], m] == (1/(2 (n - m))) (EllipticE[m]/(m - 1) + EllipticPi[n, m])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "m"], RowBox[List["EllipticPi", "[", RowBox[List["n", ",", "m"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", RowBox[List["(", RowBox[List["n", "-", "m"]], ")"]]]]], RowBox[List["(", RowBox[List[FractionBox[RowBox[List["EllipticE", "[", "m", "]"]], RowBox[List["m", "-", "1"]]], "+", RowBox[List["EllipticPi", "[", RowBox[List["n", ",", "m"]], "]"]]]], ")"]]]]]]]]

 MathML Form

 Π ( n m ) m 1 2 ( n - m ) ( E ( m ) m - 1 + Π ( n m ) ) m EllipticPi n m 1 2 n -1 m -1 EllipticE m m -1 -1 EllipticPi n m [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["m_"]]], RowBox[List["EllipticPi", "[", RowBox[List["n_", ",", "m_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[FractionBox[RowBox[List["EllipticE", "[", "m", "]"]], RowBox[List["m", "-", "1"]]], "+", RowBox[List["EllipticPi", "[", RowBox[List["n", ",", "m"]], "]"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["n", "-", "m"]], ")"]]]]]]]]]

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

 2001-10-29