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Pi




Mathematica Notation

Traditional Notation









Constants > Pi > Continued fraction representations





http://functions.wolfram.com/02.03.10.0010.01









  


  








Input Form





12/Pi^2 == 1 + 1/(3 + 16/(5 + 81/(7 + 256/(9 + 625/(11 + 1296/(13 + \[Ellipsis]))))))








Standard Form





Cell[BoxData[RowBox[List[FractionBox["12", SuperscriptBox["\[Pi]", "2"]], "\[Equal]", RowBox[List["1", "+", FractionBox["1", RowBox[List["3", "+", FractionBox["16", RowBox[List["5", "+", FractionBox["81", RowBox[List["7", "+", FractionBox["256", RowBox[List["9", "+", FractionBox["625", RowBox[List["11", "+", FractionBox["1296", RowBox[List["13", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mn> 12 </mn> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mfrac> <mo> &#10869; </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 3 </mn> <mo> + </mo> <mfrac> <mn> 16 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 5 </mn> <mo> + </mo> <mfrac> <mn> 81 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 7 </mn> <mo> + </mo> <mfrac> <mn> 256 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 9 </mn> <mo> + </mo> <mfrac> <mn> 625 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 11 </mn> <mo> + </mo> <mfrac> <mn> 1296 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 13 </mn> <mo> + </mo> <mo> &#8230; </mo> </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 /> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> 81 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> 256 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 9 </cn> <apply> <times /> <cn type='integer'> 625 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 11 </cn> <apply> <times /> <cn type='integer'> 1296 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 13 </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> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox["12", SuperscriptBox["\[Pi]", "2"]], "]"]], "\[RuleDelayed]", RowBox[List["1", "+", FractionBox["1", RowBox[List["3", "+", FractionBox["16", RowBox[List["5", "+", FractionBox["81", RowBox[List["7", "+", FractionBox["256", RowBox[List["9", "+", FractionBox["625", RowBox[List["11", "+", FractionBox["1296", RowBox[List["13", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]]]


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





2001-10-29