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Catalan




Mathematica Notation

Traditional Notation









Constants > Catalan > Continued fraction representations





http://functions.wolfram.com/02.07.10.0003.01









  


  








Input Form





Catalan == 1/2 + 1/ (2 (1/2 + 1/(1/2 + 2/(1/2 + 4/(1/2 + 6/(1/2 + 9/(1/2 + 12/(1/2 + \[Ellipsis]))))))))








Standard Form





Cell[BoxData[RowBox[List["Catalan", "\[Equal]", RowBox[List[FractionBox["1", "2"], "+", FractionBox[RowBox[List["1", "/", "2"]], RowBox[List[FractionBox["1", "2"], "+", FractionBox["1", RowBox[List[FractionBox["1", "2"], "+", FractionBox["2", RowBox[List[FractionBox["1", "2"], "+", FractionBox["4", RowBox[List[FractionBox["1", "2"], "+", FractionBox["6", RowBox[List[FractionBox["1", "2"], "+", FractionBox["9", RowBox[List[FractionBox["1", "2"], "+", FractionBox["12", RowBox[List[FractionBox["1", "2"], "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]]]]]]








MathML Form







<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> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> <mstyle scriptlevel='0'> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mn> 1 </mn> <mstyle scriptlevel='0'> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mn> 2 </mn> <mstyle scriptlevel='0'> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mn> 4 </mn> <mstyle scriptlevel='0'> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mn> 6 </mn> <mstyle scriptlevel='0'> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mn> 9 </mn> <mstyle scriptlevel='0'> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mn> 12 </mn> <mstyle scriptlevel='0'> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <ci> Catalan </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <ci> &#8230; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "Catalan", "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], "+", FractionBox["1", RowBox[List["2", " ", RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", FractionBox["1", RowBox[List[FractionBox["1", "2"], "+", FractionBox["2", RowBox[List[FractionBox["1", "2"], "+", FractionBox["4", RowBox[List[FractionBox["1", "2"], "+", FractionBox["6", RowBox[List[FractionBox["1", "2"], "+", FractionBox["9", RowBox[List[FractionBox["1", "2"], "+", FractionBox["12", RowBox[List[FractionBox["1", "2"], "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]], ")"]]]]]]]]]]]


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





2001-10-29