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 A233091 Decimal expansion of Sum_{i>=0} 1/(2*i+1)^3. 11
 1, 0, 5, 1, 7, 9, 9, 7, 9, 0, 2, 6, 4, 6, 4, 4, 9, 9, 9, 7, 2, 4, 7, 7, 0, 8, 9, 1, 3, 2, 2, 5, 1, 8, 7, 4, 1, 9, 1, 9, 3, 6, 3, 0, 0, 5, 7, 9, 7, 9, 3, 6, 5, 2, 1, 5, 6, 8, 2, 3, 7, 6, 1, 0, 9, 2, 4, 1, 0, 8, 4, 3, 0, 0, 6, 3, 0, 2, 3, 9, 5, 3, 9, 1, 3, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS J. M. Borwein, I.J. Zucker and J. Boersma, The evaluation of character Euler double sums, The Ramanujan Journal, April 2008, Volume 15, Issue 3, pp 377-405, see p. 17 c(3). R. J. Mathar, Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015, Table 22. FORMULA Equals 7*zeta(3)/8. Also equals -(1/16)*PolyGamma(2, 1/2). - Jean-François Alcover, Dec 18 2013 Equals Integral_{x=0..Pi/2} x * log(tan(x)) dx. - Amiram Eldar, Jun 29 2020 Equals Integral_{x=0..1} arcsin(x)*arccos(x)/x dx. - Amiram Eldar, Aug 03 2020 EXAMPLE 1.0517997902646449997247708913225187419193630057979365215682376109241... MATHEMATICA RealDigits[7 Zeta[3]/8, 10, 90][[1]] CROSSREFS Cf. A002117: zeta(3); A197070: 3*zeta(3)/4; A233090: 5*zeta(3)/8. Cf. A153071: sum( i >= 0, (-1)^i/(2*i+1)^3 ). Cf. A251809: sum( i >= 0, (-1)^floor(i/2)/(2*i+1)^3 ). Cf. A016755. Sequence in context: A322104 A100122 A001945 * A286941 A332459 A051854 Adjacent sequences:  A233088 A233089 A233090 * A233092 A233093 A233094 KEYWORD nonn,cons AUTHOR Bruno Berselli, Dec 04 2013 STATUS approved

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Last modified October 26 08:06 EDT 2020. Contains 338027 sequences. (Running on oeis4.)