Catalan == Integrate[ArcSinh[Cos[t]], {t, 0, Pi/2}]

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

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mi> C </mi> <annotation encoding='Mathematica'> TagBox[&quot;C&quot;, Function[Catalan]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> </msubsup> <mrow> <mrow> <msup> <mi> sinh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <ci> Catalan </ci> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </uplimit> <apply> <arcsinh /> <apply> <cos /> <ci> t </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "Catalan", "]"]], "\[RuleDelayed]", RowBox[List[SubsuperscriptBox["\[Integral]", "0", FractionBox["\[Pi]", "2"]], RowBox[List[RowBox[List["ArcSinh", "[", RowBox[List["Cos", "[", "t", "]"]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]

2001-10-29