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EllipticK




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticK[z] > Representations through more general functions > Through Meijer G > Generalized cases involving unit step theta





http://functions.wolfram.com/08.02.26.0112.01









  


  








Input Form





(UnitStep[Abs[z] - 1]/Sqrt[z + 1]) EllipticK[(z - 1)/(z + 1)] == (Pi/(2 Sqrt[2])) MeijerG[{{3/4, 3/4}, {}}, {{}, {0, 1/2}}, z, 1/2] /; !IntervalMemberQ[Interval[{-Infinity, -1}], z]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List[RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["Abs", "[", "z_", "]"]], "-", "1"]], "]"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List["z_", "-", "1"]], RowBox[List["z_", "+", "1"]]], "]"]]]], SqrtBox[RowBox[List["z_", "+", "1"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]], RowBox[List["2", " ", SqrtBox["2"]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29