A242908 Decimal expansion of exp(7*zeta(3)/(2*Pi^2)).

1, 5, 3, 1, 5, 4, 7, 0, 9, 6, 6, 8, 7, 4, 5, 7, 7, 7, 6, 6, 4, 0, 7, 7, 7, 8, 6, 5, 1, 3, 5, 8, 0, 2, 0, 6, 0, 2, 0, 1, 7, 8, 3, 3, 7, 6, 9, 0, 3, 6, 4, 8, 9, 9, 8, 8, 4, 5, 6, 2, 7, 8, 7, 1, 4, 2, 8, 8, 5, 1, 7, 5, 2, 7, 6, 9, 8, 6, 5, 6, 2, 0, 7, 8, 3, 8, 0, 2, 3, 7, 7, 6, 3, 8, 6, 3, 8, 5, 4, 1

Offset: 1

Author

Jean-François Alcover, May 26 2014

Keywords

• nonn
• cons

Examples

			1.5315470966874577766407778651358020602...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 3.10 Kneser-Mahler polynomial constants, p. 234.

Links

• Antonio Gracia Llorente, Infinite Product Formula Involving the Apery's Constant, Zenodo Preprint, 2024.
• C. J. Smyth, On measures of polynomials in several variables, Bulletin of the Australian Mathematical Society, Volume 23, Issue 1 (1981), pp. 49-63.

Crossrefs

Cf. A002117, A242909, A242910.

Programs

Mathematica

RealDigits[Exp[7*Zeta[3]/(2*Pi^2)], 10, 100] // First

Formula

M(1 + x + y + z) where M is Mahler's measure for multivariate polynomials.

Equals sqrt(2) * Product_{k>=1} (1 + 1/(4*k^2 - 1))^(4*k^2) * (1 - 2/(2*k + 1))^k. - Antonio Graciá Llorente, Sep 02 2024