OFFSET
1,1
REFERENCES
Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 2.5.2.n, pp. 186 and 223.
FORMULA
Equals (-log(4) - psi(1/4) + psi(3/4)) / 2, where psi(x) denotes the digamma function.
Equals -Integral_{x=0..1} log(x)/((1+x)*sqrt(1-x^2)) dx. - Bernard Schott, Apr 28 2021
Equals Sum_{k>=1} (-1)^(k+1)/(k*(2*k-1)). - Amiram Eldar, Jun 08 2021
From Peter Bala, Mar 05 2024: (Start)
Equals 2 * A196521.
Equals (10/3)*Integral_{x = 0..1} x/(2 - x^2*(1 - x)) dx.
Equals 5*Sum_{n >= 1} 1/(n*binomial(3*n,n)*2^n). The first 10 terms of the series gives the approximate value 0.87764914623(37...), correct to 11 decimal places. (End)
EXAMPLE
0.87764914623495130981408957018157487402308456532730...
MATHEMATICA
RealDigits[N[Pi/2 - Log[2], 105]][[10]]
PROG
(PARI) Pi/2 - log(2) \\ Michel Marcus, Mar 14 2021
CROSSREFS
KEYWORD
AUTHOR
Peter Luschny, Mar 14 2021
STATUS
approved