A239069 Decimal expansion of gamma - Ei(-1).

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

Offset: 0

Author

Jonathan Sondow, Mar 12 2014

Keywords

• cons
• nonn

Comments

See crossrefs sequences for other comments, references, links, and formulas.

Examples

			0.7965995992970531342836758655425240800732066293468...
		

References

• Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 37, table 37:7:1 at page 355.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• J. C. Lagarias, Euler's constant: Euler's work and modern developments, arXiv:1303.1856 [math.NT], 2013-2014; Bull. Amer. Math. Soc., 50 (2013), 527-628; see p. 553.

Crossrefs

Cf. A001008, A001113, A001563, A001620, A002805, A073003, A099285.

Programs

Mathematica

RealDigits[EulerGamma - ExpIntegralEi[-1], 10, 100][[1]]

PARI

Euler + eint1(1,1)[1] \\ Michel Marcus, Aug 01 2020

Formula

Equals (the Euler-Mascheroni constant) - (the exponential integral at -1) = A001620 + A099285.

Equals (the Euler-Mascheroni constant) + (Gompertz's constant / e) = A001620 + (A073003 / A001113).

Equals Sum_{n>=1} (-1)^(n-1) / A001563(n) = Sum_{n>=1} (-1)^(n-1) / (n*n!).

Equals -Integral_{x=0..1} log(x)/exp(x) dx. - Amiram Eldar, Aug 01 2020

Equals (1/e) * Sum_{k>=1} H(k)/k!, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - Amiram Eldar, Jun 25 2021