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variants of this functions
EllipticPi




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,z,m] > Integral representations > On the real axis > Of the direct function





http://functions.wolfram.com/08.06.07.0005.01









  


  








Input Form





EllipticPi[n, z, m] == (-1)^Round[Re[z]/Pi] Integrate[1/((1 - n t^2) Sqrt[1 - t^2] Sqrt[1 - m t^2]), {t, 0, Sin[z]}] + 2 Round[Re[z]/Pi] EllipticPi[n, m]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticPi", "[", RowBox[List["n_", ",", "z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]], " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", RowBox[List["Sin", "[", "z", "]"]]], RowBox[List[FractionBox["1", RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["n", " ", SuperscriptBox["t", "2"]]]]], ")"]], " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["t", "2"]]]], " ", SqrtBox[RowBox[List["1", "-", RowBox[List["m", " ", SuperscriptBox["t", "2"]]]]]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]], "+", RowBox[List["2", " ", RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]], " ", RowBox[List["EllipticPi", "[", RowBox[List["n", ",", "m"]], "]"]]]]]]]]]]


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





2007-05-02