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EllipticF






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticF[z,m] > Series representations > Generalized power series > Expansions at m==infinity





http://functions.wolfram.com/08.05.06.0075.01









  


  










Input Form





EllipticF[z, m] \[Proportional] (-1)^Round[Re[z]/Pi] (Sqrt[(-m) Sin[z]^2]/(2 m Sin[z])) (-Log[-4 m Sin[z]^2] + 2 Log[Cos[z/2]^2] (1 + O[1/m])) + Round[Re[z]/Pi] ((Log[-m]/Sqrt[-m]) (1 + O[1/m]) + ((2 Log[4])/Sqrt[-m]) (1 + O[1/m])) /; (Abs[m] -> Infinity)










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[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "m"]], " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "4"]], " ", "m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", SuperscriptBox[RowBox[List["Cos", "[", FractionBox["z", "2"], "]"]], "2"], "]"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", "m"], "]"]]]], ")"]]]]]], ")"]]]], RowBox[List["2", " ", "m", " ", RowBox[List["Sin", "[", "z", "]"]]]]], "+", RowBox[List[RowBox[List["Round", "[", FractionBox[RowBox[List["Re", "[", "z", "]"]], "\[Pi]"], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["Log", "[", RowBox[List["-", "m"]], "]"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", "m"], "]"]]]], ")"]]]], SqrtBox[RowBox[List["-", "m"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", RowBox[List["Log", "[", "4", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", "m"], "]"]]]], ")"]]]], SqrtBox[RowBox[List["-", "m"]]]]]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "m", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]










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





2007-05-02





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