A283743 Decimal expansion of Ei(1)/e, where Ei is the exponential integral function.

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

Offset

0,1

Comments

Can be considered the value of the divergent series -0! - 1! - 2! - ... ; see Lagarias reference Section 2.5. - Harry Richman, Jun 14 2020.

References

Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 44, equation 44:5:10 at page 426.

Links

Table of n, a(n) for n=0..101.

Jeffrey C. Lagarias, Euler's constant: Euler's work and modern developments, arXiv:1303.1856 [math.NT], 2013; Bull. Amer. Math. Soc., 50 (2013), 527-628.

Eric Weisstein's World of Mathematics, Exponential Integral.

Eric Weisstein's World of Mathematics, Subfactorial.

Formula

Equals Re(subfactorial(-1)) = Re(Gamma(0,-1)/e).

Equals Sum_{k=1..oo} (-1)^k*psi(k)/Gamma(k), where psi denotes the digamma function (see Spanier and Oldham). - Stefano Spezia, Jan 04 2025

Example

0.6971748832350660687654786819195515953171754309543695173200548...

Mathematica

RealDigits[ExpIntegralEi[1]/E, 10, 102][[1]]

Prog

(PARI) real(-eint1(-1)/exp(1)) \\ Michel Marcus, Jun 15 2020

Crossrefs

Cf. A000166 (subfactorials), A061382 (Pi/e, the imaginary part of subfactorial(-1)), A091725 (Ei(1)), A073003 (-exp(1)*Ei(-1)).

Sequence in context: A010725 A193594 A011480 * A339764 A229921 A145429

Adjacent sequences: A283740 A283741 A283742 * A283744 A283745 A283746

Keyword

nonn,cons,changed

Author

Jean-François Alcover, Mar 15 2017

Status

approved