A231863 - OEIS

%I #30 Sep 22 2024 17:47:50

%S 3,9,8,9,4,2,2,8,0,4,0,1,4,3,2,6,7,7,9,3,9,9,4,6,0,5,9,9,3,4,3,8,1,8,

%T 6,8,4,7,5,8,5,8,6,3,1,1,6,4,9,3,4,6,5,7,6,6,5,9,2,5,8,2,9,6,7,0,6,5,

%U 7,9,2,5,8,9,9,3,0,1,8,3,8,5,0,1,2,5,2,3,3,3,9,0,7,3,0,6,9,3,6,4,3,0,3,0,2

%N Decimal expansion of 1/sqrt(2*Pi).

%C Maximum of the probability density for standard error distribution (i.e., normal distribution density with unit variance).

%H G. C. Greubel, <a href="/A231863/b231863.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..2000 from Stanislav Sykora)

%H Amir Behrouzi-Far and Doron Zeilberger, <a href="https://arxiv.org/abs/1905.07827">On the Average Maximal Number of Balls in a Bin Resulting from Throwing r Balls into n Bins T times</a>, arXiv:1905.07827 [math.CO], 2019.

%H Marcus Michelen, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Michelen/mich3.html">A Short Note on the Average Maximal Number of Balls in a Bin</a>, Journal of Integer Sequences, Vol. 23 (2020), Article 20.1.7. See C 2,1 Table 2 p. 6. And also on <a href="https://arxiv.org/abs/1905.08933">arXiv</a>, arXiv:1905.08933 [math.CO], 2019.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Normal_density_function">Normal distribution</a>.

%H Roger Zarnowski and Charles Diminnie, <a href="http://www.pme-math.org/journal/issues/PMEJ.Vol.10.No.10.pdf">Solution to Problem 934</a>, Pi Mu Epsilon Journal, Vol. 10, No. 10 (1999), pp. 846-847.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals Integral_{x=-oo..oo} sin(Pi^2*x^2 + 1/x^2) dx (Zarnowski and Diminnie, 1999). - _Amiram Eldar_, May 21 2022

%e 0.39894228040143267793994605993438186847585863116493465766592582967...

%t RealDigits[1/Sqrt[2*Pi], 10, 100][[1]] (* _G. C. Greubel_, Jul 27 2018 *)

%o (PARI) 1/sqrt(2*Pi) \\ _G. C. Greubel_, Jul 27 2018

%o (Magma) R:= RealField(); 1/Sqrt(2*Pi(R)); // _G. C. Greubel_, Jul 27 2018

%Y Cf. A019727 (inverse), A000796 (Pi).

%K nonn,cons,easy

%O 0,1

%A _Stanislav Sykora_, Nov 14 2013