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EllipticF






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/08.05.06.0090.01









  


  










Input Form





EllipticF[z, m] == (Sin[z]/Sqrt[Sin[z]^2]) (EllipticK[m] - Cos[z] Sum[((m^k Pochhammer[1/2, k])/k!) Hypergeometric2F1[1/2, 1/2 - k, 3/2, Cos[z]^2], {k, 0, Infinity}]) + 2 Round[Re[z]/Pi] EllipticK[m] /; Abs[Cos[z]] < 1










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticF", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["Sin", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["EllipticK", "[", "m", "]"]], "-", RowBox[List[RowBox[List["Cos", "[", "z", "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["m", "k"], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k"]], "]"]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "-", "k"]], ",", FractionBox["3", "2"], ",", SuperscriptBox[RowBox[List["Cos", "[", "z", "]"]], "2"]]], "]"]]]], RowBox[List["k", "!"]]]]]]]]], ")"]]]], SqrtBox[SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]], "+", RowBox[List["2", " ", RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]], " ", RowBox[List["EllipticK", "[", "m", "]"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Cos", "[", "z", "]"]], "]"]], "<", "1"]]]]]]]]










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





2007-05-02





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