A342316 Decimal expansion of Pi/2 - log(2).

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

Offset: 1

Author

Peter Luschny, Mar 14 2021

Keywords

• nonn
• cons

Examples

			0.87764914623495130981408957018157487402308456532730...
		

References

• Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 2.5.2.n, pp. 186 and 223.

Crossrefs

Cf. A019669 (Pi/2), A002162 (log(2)), A196521.

Programs

Mathematica

RealDigits[N[Pi/2 - Log[2], 105]][[10]]

PARI

Pi/2 - log(2) \\ Michel Marcus, Mar 14 2021

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)