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 A111003 Decimal expansion of Pi^2/8. 16
 1, 2, 3, 3, 7, 0, 0, 5, 5, 0, 1, 3, 6, 1, 6, 9, 8, 2, 7, 3, 5, 4, 3, 1, 1, 3, 7, 4, 9, 8, 4, 5, 1, 8, 8, 9, 1, 9, 1, 4, 2, 1, 2, 4, 2, 5, 9, 0, 5, 0, 9, 8, 8, 2, 8, 3, 0, 1, 6, 6, 8, 6, 7, 2, 0, 2, 7, 5, 0, 5, 6, 0, 2, 8, 0, 2, 4, 0, 0, 6, 5, 5, 3, 7, 5, 2, 2, 1, 6, 7, 5, 4, 6, 4, 8, 1, 9, 0, 2, 8, 9, 7, 8, 0, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS According to Beckmann, Euler discovered the formula for this number as a sum of squares of reciprocals of odd numbers, along with similar formulas for Pi^2/6 and Pi^2/12. - Alonso del Arte, Apr 01 2013 REFERENCES Petr Beckmann, A History of Pi, 5th Ed. Boulder, Colorado: The Golem Press (1982): p. 153. George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 122. C. C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 98 L. B. W. Jolley, Summation of Series, Dover (1961). LINKS FORMULA Equals 1 + 1/(2*3) + (1/3)*(1*2)/(3*5) + (1/4)*(1*2*3)/(3*5*7) +... [Jolley eq 276] Equals Sum_{k >= 1} 1/(2*k - 1)^2 [Clawson]. - Alonso del Arte, Aug 15 2012 Equals 2*(Integral_{t=0..1} sqrt(1 - t^2) dt)^2. - Alonso del Arte, Mar 29 2013 Equals Sum_{k >= 1} 2^k/(k^2*binomial(2*k, k)). - Jean-François Alcover, Apr 29 2013 Equals Integral_{x=0..1} log((1+x^2)/(1-x^2))/x dx. - Bruno Berselli, May 13 2013 Equals limit_{p->0} integral_{x=0..Pi/2} x*tan(x)^p dx. [Jean-François Alcover, May 17 2013, after Boros & Moll p. 230] Equals A002388/8 = A102753/4 = A091476/2. - R. J. Mathar, Oct 13 2015 Equals integral_{x=0..infinity} x*K_0(x)*K_1(x)dx where K are modified Bessel functions [Gradsteyn-Ryzhik 6.576.4]. - R. J. Mathar, Oct 22 2015 Equals (3/4)*zeta(2) = (3/4)*A013661. - Wolfdieter Lang, Sep 02 2019 EXAMPLE 1.23370055013616982735431137498451889191421242590509882830166867202... 1 + 1/9 + 1/25 + 1/49 + 1/81 + 1/121 + 1/169 + 1/225 + ... - Bruno Berselli, Mar 06 2017 MATHEMATICA RealDigits[Pi^2/8, 10, 105][] (* Robert G. Wilson v *) PROG (PARI) Pi^2/8 \\ Charles R Greathouse IV, Dec 04 2016 (PARI) sumpos(n=1, (2*n-1)^-2) \\ Charles R Greathouse IV, Mar 02 2018 CROSSREFS Sequence in context: A103356 A028257 A100228 * A289277 A140182 A239472 Adjacent sequences:  A111000 A111001 A111002 * A111004 A111005 A111006 KEYWORD cons,nonn AUTHOR Sam Alexander, Oct 01 2005 EXTENSIONS More terms from Robert G. Wilson v, Oct 04 2005 STATUS approved

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Last modified October 20 02:10 EDT 2019. Contains 328244 sequences. (Running on oeis4.)