This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A069998 #67 Jun 23 2025 14:31:35
%S A069998 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,
%T A069998 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,
%U A069998 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
%N A069998 Decimal expansion of sqrt(Pi/2).
%C A069998 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
%H A069998 G. C. Greubel, <a href="/A069998/b069998.txt">Table of n, a(n) for n = 1..5000</a>
%H A069998 P. Flajolet, P. J. Grabner, P. Kirschenhofer and H. Prodinger, <a href="http://dx.doi.org/10.1016/0377-0427(93)E0258-N">On Ramanujan's Q-Function</a>, Journal of Computational and Applied Mathematics 58 (1995), 103-116.
%H A069998 I. S. Gradsteyn and I. M. Ryzhik, <a href="http://mathtable.com/gr/index.html">Table of integrals, series and products</a>, (1980), page 420 (formulas 3.757.1, 3.757.2).
%H A069998 MIT Integration Bee, <a href="https://math.mit.edu/~yyao1/pdf/2024_semifinal.pdf">2024 MIT Integration Bee - Semifinals</a>, Problem 3.
%H A069998 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A069998 From _A.H.M. Smeets_, Sep 22 2018: (Start)
%F A069998 Equals Integral_{x >= 0} sin(x)/sqrt(x) dx [see Gradsteyn and Ryzhik].
%F A069998 Equals Integral_{x >= 0} cos(x)/sqrt(x) dx [see Gradsteyn and Ryzhik]. (End)
%F A069998 Equals Integral_{x>=0} (sin(x)-x*cos(x))/x^(3/2) dx. - _Amiram Eldar_, May 08 2021
%F A069998 Equals Integral_{x=0..Pi/2} sin(cot(x)^2)*sec(x)^2 dx. See MIT link. - _Kritsada Moomuang_, Jun 23 2025
%e A069998 Sqrt(Pi/2) = 1.253314137315500251207882642... - _Wesley Ivan Hurt_, Sep 22 2016
%p A069998 Digits:=100: evalf(sqrt(Pi/2)); # _Wesley Ivan Hurt_, Sep 22 2016
%t A069998 RealDigits[Sqrt[Pi/2], 10, 120][[1]] (* _Harvey P. Dale_, Jul 24 2012 *)
%o A069998 (PARI) sqrt(Pi/2) \\ _G. C. Greubel_, Jan 09 2017
%o A069998 (PARI) intnum(x=0, [oo, -I], sin(x)/sqrt(x)) \\ _Gheorghe Coserea_, Sep 23 2018
%o A069998 (PARI) intnum(x=[0, -1/2], [oo, I], cos(x)/sqrt(x)) \\ _Gheorghe Coserea_, Sep 23 2018
%Y A069998 Cf. A064619.
%K A069998 cons,easy,nonn
%O A069998 1,2
%A A069998 _Benoit Cloitre_, May 01 2002