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Catalan




Mathematica Notation

Traditional Notation









Constants > Catalan > Series representations > Generalized power series





http://functions.wolfram.com/02.07.06.0003.01









  


  








Input Form





Catalan == 3 Sum[(1/2^(4 k)) (1/(2 (8 k + 1)^2) - 1/(2 (8 k + 2)^2) + 1/(2^2 (8 k + 3)^2) - 1/(2^3 (8 k + 5)^2) + 1/(2^3 (8 k + 6)^2) - 1/(2^4 (8 k + 7)^2)), {k, 0, Infinity}] - 2 Sum[(1/2^(12 k)) (1/(2^3 (8 k + 1)^2) + 1/(2^4 (8 k + 2)^2) + 1/(2^6 (8 k + 3)^2) - 1/(2^9 (8 k + 5)^2) - 1/(2^10 (8 k + 6)^2) - 1/(2^12 (8 k + 7)^2)), {k, 0, Infinity}]








Standard Form





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MathML Form







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<mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 1 </mn> <mrow> <msup> <mn> 2 </mn> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <ci> Catalan </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> k </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> k </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> k </ci> </apply> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> k </ci> </apply> <cn type='integer'> 5 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> k </ci> </apply> <cn type='integer'> 6 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn 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type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> k </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> k </ci> </apply> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power 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Rule Form





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





2001-10-29