A396976 Decimal expansion of (-1)*Integral_{x=0..1} log(-log(x))/(1 + x^2 + 2*x*cos(1)) dx.

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

Offset

0,3

Links

Table of n, a(n) for n=0..104.

Robert Reynolds, Derivation of some definite integrals, arXiv:2412.10395 [math.GM], 2024-2025, page 10, eq. 4.11.

Formula

Equals -(1/2)*Pi*csc(1)*log(((2 Pi)^(1/Pi)*Gamma(1/2+1/(2 Pi)))/Gamma(1/2-1/(2 Pi))).

Equals (Pi*log(cos(1/2)*Gamma(1/2 - 1/(2*Pi))^2/Pi) - log(2*Pi)) / (2*sin(1)). - Vaclav Kotesovec, Jun 13 2026

Example

0.11950929190556075544677865948768847300488651613614619...

Mathematica

RealDigits[-(1/2)*Pi Csc[1] Log[((2 Pi)^(1/Pi) Gamma[1/2+1/(2 Pi)])/Gamma[1/2-1/(2 Pi)]], 10, 105][[1]]

Prog

(PARI) -intnum(x=0, 1, log(-log(x))/(1+x^2+2*x*cos(1)))

Crossrefs

Cf. A049470, A396964.

Sequence in context: A378825 A197378 A232738 * A201395 A019881 A049256

Adjacent sequences: A396972 A396973 A396975 * A396977 A396978 A396979

Keyword

nonn,cons,new

Author

Artur Jasinski, Jun 12 2026

Status

approved