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variants of this functions
EllipticPi






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,z,m] > Series representations > Other series representations > Other expansions





http://functions.wolfram.com/08.06.06.0105.01









  


  










Input Form





EllipticPi[n, z, m] == (-1)^Round[Re[z]/Pi] Sum[((n^k Pochhammer[k + 1/2, i + j] Pochhammer[1/2, i] Pochhammer[1/2, j] m^j)/((2 k + 1) Pochhammer[k + 3/2, i + j] i! j!)) Sin[z]^(2 i + 2 j + 2 k + 1), {k, 0, Infinity}, {i, 0, Infinity}, {j, 0, Infinity}] + 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[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["n", "k"], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["k", "+", FractionBox["1", "2"]]], ",", RowBox[List["i", "+", "j"]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "i"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "j"]], "]"]], " ", SuperscriptBox["m", "j"]]], ")"]], " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], RowBox[List[RowBox[List["2", " ", "i"]], "+", RowBox[List["2", " ", "j"]], "+", RowBox[List["2", " ", "k"]], "+", "1"]]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["k", "+", FractionBox["3", "2"]]], ",", RowBox[List["i", "+", "j"]]]], "]"]], " ", RowBox[List["i", "!"]], " ", RowBox[List["j", "!"]]]]]]]]]]]]], "+", 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





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