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

0,1

Comments

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

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.

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

Example

0.7965995992970531342836758655425240800732066293468...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A199471 A385695 A200098 * A154168 A389356 A019644

Adjacent sequences: A239066 A239067 A239068 * A239070 A239071 A239072

Keyword

cons,nonn

Author

Jonathan Sondow, Mar 12 2014

Status

approved