This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A233091 #38 Feb 03 2025 09:48:42
%S A233091 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,
%T A233091 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,
%U A233091 0,8,4,3,0,0,6,3,0,2,3,9,5,3,9,1,3,1
%N A233091 Decimal expansion of Sum_{i>=0} 1/(2*i+1)^3.
%C A233091 This constant is irrational. - _Charles R Greathouse IV_, Feb 03 2025
%D A233091 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.3, p. 42.
%H A233091 J. M. Borwein, I.J. Zucker, and J. Boersma, <a href="http://carma.newcastle.edu.au/MZVs/mzv-week05.pdf">The evaluation of character Euler double sums</a>, The Ramanujan Journal, April 2008, Volume 15, Issue 3, pp 377-405, see p. 17 c(3).
%H A233091 R. J. Mathar, <a href="http://arxiv.org/abs/1008.2547">Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli</a>, arXiv:1008.2547 [math.NT], 2010-2015, Table 22.
%F A233091 Equals 7*zeta(3)/8.
%F A233091 Also equals -(1/16)*PolyGamma(2, 1/2). - _Jean-François Alcover_, Dec 18 2013
%F A233091 Equals Integral_{x=0..Pi/2} x * log(tan(x)) dx. - _Amiram Eldar_, Jun 29 2020
%F A233091 Equals Integral_{x=0..1} arcsin(x)*arccos(x)/x dx. - _Amiram Eldar_, Aug 03 2020
%e A233091 1.0517997902646449997247708913225187419193630057979365215682376109241...
%t A233091 RealDigits[7 Zeta[3]/8, 10, 90][[1]]
%o A233091 (PARI) 7*zeta(3)/8 \\ _Stefano Spezia_, Oct 31 2024
%Y A233091 Cf. A002117: zeta(3); A197070: 3*zeta(3)/4; A233090: 5*zeta(3)/8.
%Y A233091 Cf. A153071: sum( i >= 0, (-1)^i/(2*i+1)^3 ).
%Y A233091 Cf. A251809: sum( i >= 0, (-1)^floor(i/2)/(2*i+1)^3 ).
%Y A233091 Cf. A016755.
%K A233091 nonn,cons
%O A233091 1,3
%A A233091 _Bruno Berselli_, Dec 04 2013