Catalan == (1/4) LerchPhi[-1, 2, 1/2]

Cell[BoxData[RowBox[List["Catalan", "\[Equal]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["LerchPhi", "[", RowBox[List[RowBox[List["-", "1"]], ",", "2", ",", FractionBox["1", "2"]]], "]"]]]]]]]]

<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> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#934; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[CapitalPhi]&quot;, &quot;(&quot;, RowBox[List[TagBox[RowBox[List[&quot;-&quot;, &quot;1&quot;]], Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;2&quot;, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;1&quot;, &quot;2&quot;], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[LerchPhi[Slot[1], Slot[2], Slot[3]]]]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <ci> Catalan </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <ci> LerchPhi </ci> <cn type='integer'> -1 </cn> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "Catalan", "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["LerchPhi", "[", RowBox[List[RowBox[List["-", "1"]], ",", "2", ",", FractionBox["1", "2"]]], "]"]]]]]]]]

2001-10-29