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/02.07.07.0039.01

 Input Form

 Catalan == (Pi/4) Log[2] + 2 Integrate[Log[Cosh[t]] Sech[2 t], {t, 0, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List["Catalan", "\[Equal]", RowBox[List[RowBox[List[FractionBox["\[Pi]", "4"], " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["2", " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List["Log", "[", RowBox[List["Cosh", "[", "t", "]"]], "]"]], " ", RowBox[List["Sech", "[", RowBox[List["2", " ", "t"]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]]]

 MathML Form

 C TagBox["C", Function[Catalan]] 2 0 log ( cosh ( t ) ) sech ( 2 t ) t + π 4 log ( 2 ) Catalan 2 t 0 t 2 t 4 -1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "Catalan", "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["Log", "[", "2", "]"]]]], "+", RowBox[List["2", " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List["Cosh", "[", "t", "]"]], "]"]], " ", RowBox[List["Sech", "[", RowBox[List["2", " ", "t"]], "]"]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]]]

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

 2001-10-29