A224518 Decimal expansion of Integral_{x=0..Infinity} exp(-x)/(1+x^2) dx.

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

Offset

0,1

References

Konrad Knopp, Theory and application of infinite series, Blackie & Son Limited, London and Glasgow, 1954. See p. 553.

Links

Table of n, a(n) for n=0..99.

Steven R. Finch, Errata and addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2024, p. 62.

Formula

Equals (Pi/2)*cos(1) + cosIntegral(1)*sin(1) - cos(1)*sinIntegral(1).

Equals Integral_{x=0..1} 1/(1+log(x)^2) dx.

Equals Integral_{x=0..Pi/2} exp(-tan(x)) dx. - Amiram Eldar, Aug 06 2020

Equals Integral_{x=0..oo} arctan(x)/exp(x) dx. - Kritsada Moomuang, Oct 24 2025

Example

0.621449624235813357639265728215339323893164676919705416947975531641930561621...

Mathematica

(Pi/2)*Cos[1] + CosIntegral[1]*Sin[1] - Cos[1]*SinIntegral[1] // RealDigits[#, 10, 100]& // First
RealDigits[Integrate[Exp[-x]/(1+x^2), {x, 0, \[Infinity]}], 10, 120][[1]] (* Harvey P. Dale, Jan 04 2026 *)

Crossrefs

Sequence in context: A101607 A039508 A324569 * A375741 A363684 A393649

Adjacent sequences: A224515 A224516 A224517 * A224519 A224520 A224521

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 09 2013

Status

approved