A396964 Decimal expansion of (-1)*Integral_{x=0..1} log(-log(x))/(1 + x^2 + 2*x*cos(4)) dx.

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

Offset

1,3

Links

Table of n, a(n) for n=1..105.

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(4)*log((2*Pi)^(2 - 4/Pi)*Gamma(3/2 - 2/Pi)/Gamma(-1/2 + 2/Pi)).

Example

1.02756386551864675847502033400582086722448311493...

Mathematica

RealDigits[(-1)*Integrate[Log[-Log[x]]/(1 + x^2 + 2 x Cos[4]), {x, 0, 1}], 10, 105][[1]]
(* Alternative: *)
RealDigits[(1/2)*Pi Csc[4] Log[((2 Pi)^(2 - 4/Pi) Gamma[3/2 - 2/Pi])/Gamma[-1/2 + 2/Pi]], 10, 105][[1]]

Prog

(PARI) -intnum(x=0, 1, log(-log(x))/(1+x^2+2*x*cos(4)))

Crossrefs

Cf. A396976.

Sequence in context: A151856 A248223 A019825 * A097157 A181320 A195450

Adjacent sequences: A396960 A396962 A396963 * A396965 A396966 A396967

Keyword

nonn,cons

Author

Artur Jasinski, Jun 11 2026

Status

approved