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A072691
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Decimal expansion of Pi^2/12.
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9
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8, 2, 2, 4, 6, 7, 0, 3, 3, 4, 2, 4, 1, 1, 3, 2, 1, 8, 2, 3, 6, 2, 0, 7, 5, 8, 3, 3, 2, 3, 0, 1, 2, 5, 9, 4, 6, 0, 9, 4, 7, 4, 9, 5, 0, 6, 0, 3, 3, 9, 9, 2, 1, 8, 8, 6, 7, 7, 7, 9, 1, 1, 4, 6, 8, 5, 0, 0, 3, 7, 3, 5, 2, 0, 1, 6, 0, 0, 4, 3, 6, 9, 1, 6, 8, 1, 4, 4, 5, 0, 3, 0, 9, 8, 7, 9, 3, 5, 2, 6, 5, 2, 0, 0, 2
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OFFSET
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0,1
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COMMENTS
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Also -dilogarithm(-1). - Rick L. Shepherd, Jul 21 2004
Also zeta(1,1), the double zeta-function with both arguments equal to 1. - R. J. Mathar, Oct 10 2011
Also zeta(2)/2. [Jean-François Alcover, May 17 2013]
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REFERENCES
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C. C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 98
Jolley, Summation of Series, Dover (1961) eq. (234) page 44.
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LINKS
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Table of n, a(n) for n=0..104.
Eric Weisstein's World of Mathematics, Dilogarithm
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FORMULA
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= 1/(1*2)+ 1/(2*4) + 1/(3*6)+ 1/(4*8)+ ... [Jolley]
Sum_{n>=1} ((-1)^(n+1))/n^2 [Clawson]. - Alonso del Arte, Aug 15 2012
Equals integral(x=0..1) log((1+x^3)/(1-x^3))/x dx. [Bruno Berselli, May 13 2013]
Equals integral(x=1..2) log(x)/(x-1) dx. [Jean-François Alcover, May 17 2013]
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EXAMPLE
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0.822467033424113218236207583323... = A013661/2.
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MATHEMATICA
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RealDigits[Pi^2/12, 10, 105][[1]] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A072692 (Pi^2/12 is in asymptotic formula related to sigma(n), A000203).
Sequence in context: A037920 A138997 A133918 * A021928 A185111 A086058
Adjacent sequences: A072688 A072689 A072690 * A072692 A072693 A072694
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KEYWORD
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cons,nonn,changed
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AUTHOR
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Rick L. Shepherd, Jul 02 2002
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STATUS
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approved
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