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variants of this functions
EllipticPi






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,z,m] > Integration > Indefinite integration > Involving only one direct function





http://functions.wolfram.com/08.06.21.0001.01









  


  










Input Form





Integrate[EllipticPi[n, z, m], z] == Sum[(((-1)^(k + j + l - 1) m^l n^k 2^(-2 k - 2 j - 2 l))/ ((1 + 2 j + 2 k + 2 l) j! l!)) Pochhammer[1/2, j] Pochhammer[1/2, l] Sum[(-1)^p Binomial[2 k + 2 j + 2 l + 1, p] (Cos[(1 + 2 j + 2 k + 2 l - 2 p) z]/(1 + 2 j + 2 k + 2 l - 2 p)), {p, 0, k + j + l}], {j, 0, Infinity}, {l, 0, Infinity}, {k, 0, Infinity}]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["EllipticPi", "[", RowBox[List["n_", ",", "z_", ",", "m_"]], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["l", "=", "0"]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["k", "+", "j", "+", "l", "-", "1"]]], " ", SuperscriptBox["m", "l"], " ", SuperscriptBox["n", "k"], " ", SuperscriptBox["2", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "-", RowBox[List["2", " ", "j"]], "-", RowBox[List["2", " ", "l"]]]]]]], ")"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "j"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "l"]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["p", "=", "0"]], RowBox[List["k", "+", "j", "+", "l"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "p"], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List[RowBox[List["2", " ", "k"]], "+", RowBox[List["2", " ", "j"]], "+", RowBox[List["2", " ", "l"]], "+", "1"]], ",", "p"]], "]"]], " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "j"]], "+", RowBox[List["2", " ", "k"]], "+", RowBox[List["2", " ", "l"]], "-", RowBox[List["2", " ", "p"]]]], ")"]], " ", "z"]], "]"]]]], RowBox[List["1", "+", RowBox[List["2", " ", "j"]], "+", RowBox[List["2", " ", "k"]], "+", RowBox[List["2", " ", "l"]], "-", RowBox[List["2", " ", "p"]]]]]]]]], RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "j"]], "+", RowBox[List["2", " ", "k"]], "+", RowBox[List["2", " ", "l"]]]], ")"]], " ", RowBox[List["j", "!"]], " ", RowBox[List["l", "!"]]]]]]]]]]]]]]]










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





2001-10-29





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