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 EllipticK

 http://functions.wolfram.com/08.02.27.0003.01

 Input Form

 EllipticK[2] == ((-Pi^2) EllipticE[2] + Sqrt[2] Pi^(3/2) Gamma[3/4]^2)/ (2 Gamma[3/4]^4)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["EllipticK", "[", "2", "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[Pi]", "2"]]], " ", RowBox[List["EllipticE", "[", "2", "]"]]]], "+", RowBox[List[SqrtBox["2"], SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "4"]]]]]]]]

 MathML Form

 K ( 2 ) 2 π 3 / 2 Γ ( 3 4 ) 2 - π 2 E ( 2 ) 2 Γ ( 3 4 ) 4 EllipticK 2 2 1 2 3 2 Gamma 3 4 2 -1 2 EllipticE 2 2 Gamma 3 4 4 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticK", "[", "2", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[Pi]", "2"]]], " ", RowBox[List["EllipticE", "[", "2", "]"]]]], "+", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "4"]]]]]]]]

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

 2007-05-02