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 EllipticPi

 http://functions.wolfram.com/08.06.07.0003.01

 Input Form

 EllipticPi[n, z, m] == Integrate[1/(1 - n JacobiSN[t, m]^2), {t, 0, EllipticF[z, m]}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["EllipticPi", "[", RowBox[List["n", ",", "z", ",", "m"]], "]"]], "\[Equal]", RowBox[List[SubsuperscriptBox["\[Integral]", "0", RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]]], RowBox[List[FractionBox["1", RowBox[List["1", "-", RowBox[List["n", " ", SuperscriptBox[RowBox[List["JacobiSN", "[", RowBox[List["t", ",", "m"]], "]"]], "2"]]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]

 MathML Form

 Π ( n ; z m ) 0 F ( z m ) 1 1 - n sn ( t m ) 2 t EllipticPi n z m t 0 EllipticF z m 1 1 -1 n JacobiSN t m 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticPi", "[", RowBox[List["n_", ",", "z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SubsuperscriptBox["\[Integral]", "0", RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]]], RowBox[List[FractionBox["1", RowBox[List["1", "-", RowBox[List["n", " ", SuperscriptBox[RowBox[List["JacobiSN", "[", RowBox[List["t", ",", "m"]], "]"]], "2"]]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]

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

 2001-10-29