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A233091 Decimal expansion of Sum_{i>=0} 1/(2*i+1)^3. 13
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: A001945 A342921 A342417 * A286941 A332459 A051854
KEYWORD
nonn,cons
AUTHOR
Bruno Berselli, Dec 04 2013
STATUS
approved

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Last modified March 29 08:01 EDT 2024. Contains 371265 sequences. (Running on oeis4.)