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variants of this functions
EllipticPi






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,z,m] > Series representations > Generalized power series > Expansions at n==1





http://functions.wolfram.com/08.06.06.0016.01









  


  










Input Form





EllipticPi[n, z, m] \[Proportional] Round[Re[z]/Pi] (Pi/(Sqrt[1 - m/n] Sqrt[1 - n])) + ((-1)^Round[Re[z]/Pi] Sin[z] AppellF1[1/2, 3/2, 1/2, 3/2, Sin[z]^2, m Sin[z]^2] + Round[Re[z]/Pi] ((2 EllipticE[m])/(m - 1) + 2 EllipticK[m])) (1 + O[n - 1]) /; !Element[(Pi + 2 Re[z])/(4 Pi), Integers]










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[FractionBox[RowBox[List[RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]], " ", "\[Pi]"]], RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["m", "n"]]]], " ", SqrtBox[RowBox[List["1", "-", "n"]]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]], " ", RowBox[List["Sin", "[", "z", "]"]], " ", RowBox[List["AppellF1", "[", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "2"], ",", FractionBox["1", "2"], ",", FractionBox["3", "2"], ",", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"], ",", RowBox[List["m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]]], "]"]]]], "+", RowBox[List[RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["EllipticE", "[", "m", "]"]]]], RowBox[List["m", "-", "1"]]], "+", RowBox[List["2", " ", RowBox[List["EllipticK", "[", "m", "]"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["n", "-", "1"]], "]"]]]], ")"]]]]]], "/;", RowBox[List["!", RowBox[List[FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["2", " ", RowBox[List["Re", "[", "z", "]"]]]]]], RowBox[List["4", " ", "\[Pi]"]]], "\[Element]", "Integers"]]]]]]]]]]










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





2007-05-02





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