html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Catalan

 http://functions.wolfram.com/02.07.07.0044.01

 Input Form

 Catalan == (-(Pi/4)) Log[2] - (1/2) Integrate[Log[1 - Cos[t]], {t, 0, Pi/2}]

 Standard Form

 Cell[BoxData[RowBox[List["Catalan", "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "4"]]], " ", RowBox[List["Log", "[", "2", "]"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", FractionBox["\[Pi]", "2"]], RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["Cos", "[", "t", "]"]]]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]]]

 MathML Form

 C TagBox["C", Function[Catalan]] - 1 2 0 π 2 log ( 1 - cos ( t ) ) t - π 4 log ( 2 ) Catalan -1 1 2 t 0 2 -1 1 -1 t -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[FractionBox["1", "2"], " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", FractionBox["\[Pi]", "2"]], RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["Cos", "[", "t", "]"]]]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]]]

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

 2001-10-29