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 Catalan

 http://functions.wolfram.com/02.07.07.0037.01

 Input Form

 Catalan == (-(Pi/4)) Log[2] + 4 Integrate[(t Log[t + 1/t])/(1 + t^4), {t, 1, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List["Catalan", "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "4"]]], " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["4", " ", RowBox[List[SubsuperscriptBox["\[Integral]", "1", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List["t", " ", RowBox[List["Log", "[", RowBox[List["t", "+", FractionBox["1", "t"]]], "]"]]]], RowBox[List["1", "+", SuperscriptBox["t", "4"]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]]]

 MathML Form

 C TagBox["C", Function[Catalan]] 4 1 t t 4 + 1 log ( t + 1 t ) t - π 4 log ( 2 ) Catalan 4 t 1 t t 4 1 -1 t 1 t -1 -1 4 -1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "Catalan", "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["-", "\[Pi]"]], ")"]], " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["4", " ", RowBox[List[SubsuperscriptBox["\[Integral]", "1", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List["t", " ", RowBox[List["Log", "[", RowBox[List["t", "+", FractionBox["1", "t"]]], "]"]]]], RowBox[List["1", "+", SuperscriptBox["t", "4"]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]]]

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

 2001-10-29

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