A086058 Decimal expansion of conjectured value of delta related to the Masser-Gramain constant.

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

Offset: 1

Author

Eric W. Weisstein, Jul 07 2003

Keywords

• nonn
• cons

Comments

Numerical work by Melquiond et al. (see reference) disproves Gramain's conjecture, correct bounds for the Masser-Gramain constant delta are: 1.819776 < delta < 1.819833. - Vaclav Kotesovec, Apr 27 2015

Examples

			1.82282524967884703299532871626146494947569311889485021839381561303709...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 7.2, p. 460.

Links

• Guillaume Melquiond, W. Georg Nowak, Paul Zimmermann, Numerical approximation of the Masser-Gramain constant to four decimal places, Mathematics of Computation, Volume 82, Number 282, April 2013, Pages 1235-1246.
• Eric Weisstein's World of Mathematics, Masser-Gramain Constant.

Crossrefs

Cf. A062089, A241017.

Programs

Mathematica

RealDigits[ 1 + 2*EulerGamma + 2*Log[2] + 3*Log[Pi] - 4*Log[Gamma[1/4]], 10, 102] // First (* Jean-François Alcover, Feb 07 2013, after Eric W. Weisstein *)

PARI

1+2*Euler+2*log(2)+3*log(Pi)-4*lngamma(1/4) \\ Charles R Greathouse IV, Dec 08 2014

Formula

Equals 1 + A241017.

Equals 1 + A062089/Pi.