A256425 Decimal expansion of the generalized Euler constant gamma(1,3).

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

Offset: 0

Author

N. J. A. Sloane, Apr 09 2015

Keywords

• nonn
• cons

Examples

			0.67780716378423221053372461245491438316931257963255620415268...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.5.3, p. 32.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975), 125-142. [gamma=A001620, gamma(0,2)=A239097, gamma(1,2)=A228725, N_k=A007947, gamma(1,3)=A256425, the present sequence]

Crossrefs

Cf. A001620, A002391, A007947, A047787, A228725, A239097.

Programs

Mathematica

RealDigits[EulerGamma/3 + Pi*Sqrt[3]/18 + Log[3]/6, 10, 50][[1]] (* G. C. Greubel, Jun 08 2017 *)

PARI

Euler/3 + Pi*sqrt(3)/18 + log(3)/6 \\ Charles R Greathouse IV, Sep 08 2015

PARI

-(psi(1/3) + log(3))/3 \\ Charles R Greathouse IV, Feb 03 2025

Formula

Equals gamma/3+Pi*sqrt(3)/18+log(3)/6.

Equals -(psi(1/3) + log(3))/3 = (A047787 - A002391)/3. - Amiram Eldar, Jan 07 2024