A327121 Decimal expansion of Sum_{k>=1} 1/k + exp(k) * Ei(-k), where Ei(x) is the exponential integral of the first kind.

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

Offset

0,1

Comments

This constant is introduced in the paper by Sampedro.

Links

Table of n, a(n) for n=0..86.

Juan Carlos Sampedro, On a new constant related to Euler's constant, The Ramanujan Journal, Vol. 46, No. 1 (2018), pp. 77-89.

Eric Weisstein's World of Mathematics, Exponential Integral.

Formula

Equals Integral_{x=0..oo} log(Gamma(x)) * exp(-x) dx. See the paper by Sampedro for other formulas.

Example

0.843302107531977964096996817154768683383574924252925...

Mathematica

RealDigits[N[Integrate[Exp[-x]*Log[Gamma[x]], {x, 0, Infinity}], 100], 10, 100][[1]]

Crossrefs

Cf. A001620.

Sequence in context: A109595 A256782 A071832 * A091475 A197482 A292529

Adjacent sequences: A327118 A327119 A327120 * A327122 A327123 A327124

Keyword

nonn,cons

Author

Amiram Eldar, Sep 14 2019

Status

approved