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

1,1

References

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

Links

Table of n, a(n) for n=1..102.

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

Example

0.87764914623495130981408957018157487402308456532730...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A210462 A010529 A201505 * A219388 A177218 A342374

Adjacent sequences: A342313 A342314 A342315 * A342317 A342318 A342319

Keyword

nonn,cons

Author

Peter Luschny, Mar 14 2021

Status

approved