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A094642 Decimal expansion of log(Pi/2). 8
4, 5, 1, 5, 8, 2, 7, 0, 5, 2, 8, 9, 4, 5, 4, 8, 6, 4, 7, 2, 6, 1, 9, 5, 2, 2, 9, 8, 9, 4, 8, 8, 2, 1, 4, 3, 5, 7, 1, 7, 9, 4, 6, 7, 8, 5, 5, 5, 0, 5, 6, 3, 1, 7, 3, 9, 2, 9, 4, 3, 0, 6, 1, 9, 7, 8, 7, 4, 4, 1, 4, 7, 9, 1, 5, 1, 3, 1, 3, 6, 4, 1, 7, 7, 7, 5, 9, 9, 4, 3, 2, 7, 9, 0, 7, 1, 0, 2, 0, 1, 6, 0, 0, 0, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

G. Boros and V. Moll, Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge University Press, Cambridge, 2004, Chap. 7.

J. Borwein and P. Borwein, Pi and the AGM, John Wiley & Sons, New York, 1987, Chap. 11.

LINKS

Table of n, a(n) for n=0..104.

D. Huylebrouck, Similarities in irrationality proofs for Pi, ln2, zeta(2) and zeta(3), Amer. Math. Monthly 108 (2001) 222-231.

J. Sondow, A faster product for pi and a new integral for ln(pi/2), Amer. Math. Monthly 112 (2005), 729-734 and 113 (2006), 670.

FORMULA

Equals Sum_{n>=1} zeta(2*n)/(n*2^(2*n) (cf. Boros & Moll p. 131). - Jean-Fran├žois Alcover, Apr 29 2013

Equals Re(log(log(I))). - Stanislav Sykora, May 09 2015

Equals Integral_{-infinity..+infinity} -log(1/2 + i*z)/cosh(Pi*z) dz, where i is the imaginary unit. - Peter Luschny, Apr 08 2018

Equals Integral_{0..Pi/2} (2/(Pi-2*t)-tan(t)) dt. - Clark Kimberling, Jul 10 2020

Equals -Sum_{k>=1} log(1 - 1/(2*k)^2). - Amiram Eldar, Aug 12 2020

EXAMPLE

log(Pi/2) = 0.4515827...

MATHEMATICA

RealDigits[ Log[Pi/2], 10, 111][[1]]

PROG

(PARI) log(Pi/2) \\ Charles R Greathouse IV, Jun 23 2014

CROSSREFS

Cf. A094643.

Sequence in context: A073241 A336888 A336885 * A069284 A272638 A299630

Adjacent sequences:  A094639 A094640 A094641 * A094643 A094644 A094645

KEYWORD

cons,easy,nonn

AUTHOR

Jonathan Sondow and Robert G. Wilson v, May 18 2004

STATUS

approved

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Last modified April 17 05:12 EDT 2021. Contains 343059 sequences. (Running on oeis4.)