OFFSET
1,2
COMMENTS
This constant, sqrt(Pi/2), appears in one of the formulations of the Birthday Problem: An asymptotic expansion of the expected value for the average number of people required to find a pair having the same birthday out of k possible birthdays is sqrt(Pi/2)*sqrt(k) + 2/3 + 1/12*sqrt(Pi/2)*sqrt(1/k) - 4/135*1/k + ... found by the Indian mathematician Srinivasa Ramanujan (1887-1920). - Martin Renner, Sep 14 2016
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
P. Flajolet, P. J. Grabner, P. Kirschenhofer and H. Prodinger, On Ramanujan's Q-Function, Journal of Computational and Applied Mathematics 58 (1995), 103-116.
I. S. Gradsteyn and I. M. Ryzhik, Table of integrals, series and products, (1980), page 420 (formulas 3.757.1, 3.757.2).
FORMULA
From A.H.M. Smeets, Sep 22 2018: (Start)
Equals Integral_{x >= 0} sin(x)/sqrt(x) dx [see Gradsteyn and Ryzhik].
Equals Integral_{x >= 0} cos(x)/sqrt(x) dx [see Gradsteyn and Ryzhik]. (End)
Equals Integral_{x>=0} (sin(x)-x*cos(x))/x^(3/2) dx. - Amiram Eldar, May 08 2021
EXAMPLE
Sqrt(Pi/2) = 1.253314137315500251207882642... - Wesley Ivan Hurt, Sep 22 2016
MAPLE
Digits:=100: evalf(sqrt(Pi/2)); # Wesley Ivan Hurt, Sep 22 2016
MATHEMATICA
RealDigits[Sqrt[Pi/2], 10, 120][[1]] (* Harvey P. Dale, Jul 24 2012 *)
PROG
(PARI) sqrt(Pi/2) \\ G. C. Greubel, Jan 09 2017
(PARI) intnum(x=0, [oo, -I], sin(x)/sqrt(x)) \\ Gheorghe Coserea, Sep 23 2018
(PARI) intnum(x=[0, -1/2], [oo, I], cos(x)/sqrt(x)) \\ Gheorghe Coserea, Sep 23 2018
CROSSREFS
KEYWORD
AUTHOR
Benoit Cloitre, May 01 2002
STATUS
approved