login
A372919
Decimal expansion of (Pi/4)*log(2) + Catalan.
0
1, 4, 6, 0, 3, 6, 2, 1, 1, 6, 7, 5, 3, 1, 1, 9, 5, 4, 7, 6, 7, 9, 7, 7, 5, 7, 3, 9, 4, 9, 1, 7, 8, 7, 5, 9, 7, 6, 0, 8, 7, 9, 5, 2, 9, 9, 3, 7, 3, 9, 9, 3, 7, 0, 7, 8, 4, 7, 9, 4, 6, 9, 3, 2, 9, 2, 0, 3, 4, 0, 1, 5, 7, 0, 7, 0, 4, 4, 0, 2, 6, 6, 0, 8, 6, 9, 3, 8, 7, 5, 3, 3, 2, 8, 7
OFFSET
1,2
LINKS
Paul J. Nahin, Inside interesting integrals, Undergrad. Lecture Notes in Physics, Springer (2020), (5.1.3).
Michael I. Shamos, Shamos's catalog of the real numbers, 2011. See p. 465.
FORMULA
Equals Integral_{x=0..oo} log(x+1)/(x^2+1) dx = A086054/4 + A006752.
From Amiram Eldar, May 21 2024: (Start)
Formulas from Shamos (2011):
Equals Integral_{x>=1} log(x^2-1)/(x^2+1) dx.
Equals Integral_{x>=0} x/(exp(x) + 2*exp(-x) - 2) dx.
Equals Integral_{x=0..Pi/2} (sin(x)-cos(x))/(sin(x)+cos(x)) * x dx.
Equals Integral_{x>=0} arccot(x)/(x+1) dx.
Equals Integral_{x=0..Pi/2} log(1+tan(x)) dx. (End)
EXAMPLE
1.46036211...
MAPLE
Pi/4*log(2)+Catalan ; evalf(%) ;
MATHEMATICA
RealDigits[Pi*Log[2]/4 + Catalan, 10, 120][[1]] (* Amiram Eldar, May 21 2024 *)
CROSSREFS
Sequence in context: A319091 A328227 A059750 * A243983 A117036 A016723
KEYWORD
cons,nonn
AUTHOR
R. J. Mathar, May 16 2024
STATUS
approved