A233091 Decimal expansion of Sum_{i>=0} 1/(2*i+1)^3.

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

Offset: 1

Author

Bruno Berselli, Dec 04 2013

Keywords

• nonn
• cons

Comments

This constant is irrational. - Charles R Greathouse IV, Feb 03 2025

Examples

			1.0517997902646449997247708913225187419193630057979365215682376109241...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.3, p. 42.

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.

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.

Programs

Mathematica

RealDigits[7 Zeta[3]/8, 10, 90][[1]]

PARI

7*zeta(3)/8 \\ Stefano Spezia, Oct 31 2024

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