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 A072691 Decimal expansion of Pi^2/12. 38
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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 Lim_{n->infinity} A244583(n)/prime(n)^2. See A244583 for details. - Richard R. Forberg, Jan 04 2015 REFERENCES C. C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 98 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.11 p. 126 and section 8.5 p. 501. Jolley, Summation of Series, Dover (1961) eq. (234) page 44. LINKS Ivan Panchenko, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Dilogarithm FORMULA Equals 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 EXAMPLE 0.822467033424113218236207583323... = A013661/2. MATHEMATICA RealDigits[Pi^2/12, 10, 105][[1]] (* Robert G. Wilson v *) PROG (PARI) zeta(2)/2 \\ Michel Marcus, Sep 08 2014 (PARI) -dilog(-1) \\ Charles R Greathouse IV, Apr 17 2015 (PARI) Pi^2/12 \\ Charles R Greathouse IV, Apr 17 2015 (PARI) zetamult([1, 1]) \\ Charles R Greathouse IV, Apr 17 2015 (Python) from mpmath import * mp.dps=106 print map(int, list(str(zeta(2)/2))[2:-1]) # Indranil Ghosh, Jul 08 2017 CROSSREFS Cf. A072692 (Pi^2/12 is in asymptotic formula related to sigma(n), A000203). Cf. A113319 (sum_{i>=0} 1/(i^2+1)); A232883 (sum_{i>=0} 1/(2*i^2+1)). Sequence in context: A138997 A248498 A133918 * A021928 A185111 A086058 Adjacent sequences:  A072688 A072689 A072690 * A072692 A072693 A072694 KEYWORD nonn,cons AUTHOR Rick L. Shepherd, Jul 02 2002 STATUS approved

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Last modified November 18 01:20 EST 2018. Contains 317279 sequences. (Running on oeis4.)