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

Author

Jean-François Alcover, Mar 15 2017

Keywords

• nonn
• cons

Comments

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

Examples

			0.6971748832350660687654786819195515953171754309543695173200548...
		

References

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

Links

• 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.

Crossrefs

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

Programs

Mathematica

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

PARI

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

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