|
|
A069998
|
|
Decimal expansion of sqrt(Pi/2).
|
|
9
|
|
|
1, 2, 5, 3, 3, 1, 4, 1, 3, 7, 3, 1, 5, 5, 0, 0, 2, 5, 1, 2, 0, 7, 8, 8, 2, 6, 4, 2, 4, 0, 5, 5, 2, 2, 6, 2, 6, 5, 0, 3, 4, 9, 3, 3, 7, 0, 3, 0, 4, 9, 6, 9, 1, 5, 8, 3, 1, 4, 9, 6, 1, 7, 8, 8, 1, 7, 1, 1, 4, 6, 8, 2, 7, 3, 0, 3, 9, 2, 0, 9, 8, 7, 4, 7, 3, 2, 9, 7, 9, 1, 9, 1, 8, 9, 0, 2, 8, 6, 3, 3, 0, 5, 8, 0, 0, 4
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
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.
|
|
FORMULA
|
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
|
|
|
MAPLE
|
|
|
MATHEMATICA
|
RealDigits[Sqrt[Pi/2], 10, 120][[1]] (* Harvey P. Dale, Jul 24 2012 *)
|
|
PROG
|
(PARI) intnum(x=[0, -1/2], [oo, I], cos(x)/sqrt(x)) \\ Gheorghe Coserea, Sep 23 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|