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 A103647 #29 Feb 16 2025 08:32:56 %S A103647 4,8,3,9,4,1,4,4,9,0,3,8,2,8,6,6,9,9,5,9,5,6,6,0,3,8,5,8,7,1,1,2,1,3, %T A103647 0,9,6,5,7,3,4,3,9,4,1,4,7,4,8,7,0,0,5,0,9,7,5,1,1,0,1,6,8,5,6,2,2,0, %U A103647 0,1,2,7,1,4,0,1,6,6,5,8,9,0,1,6,6,2,2,5,8,9,3,8,7,8,8,4,8,0,9,4,5,8,2,7,4 %N A103647 Decimal expansion of area of the largest rectangle under the normal curve. %C A103647 The normal curve is 'nc' = 1/(sqrt(2*Pi))*e^(-1/2*x^2). Area = 2*x*nc. d(Area)/dx = (sqrt(2/Pi) - sqrt(2/Pi)*x^2)*e^(-1/2*x^2). Maximum at x = 1. %C A103647 Occurs in a formula estimating the error in approximating a binomial distribution with a Poisson distribution. See [Prohorov]. - _Eric M. Schmidt_, Feb 26 2014 %D A103647 R. E. Larson, R. P. Hostetler & B. H. Edwards, Calculus of a Single Variable, 5th Edition, D. C. Heath and Co., Lexington, MA Section 5.4 Exponential Functions: Differentiation and Integration, Exercise 61, page 351. %D A103647 Yu. V. Prohorov, Asymptotic behavior of the binomial distribution. 1961. Select. Transl. Math. Statist. and Probability, Vol. 1 pp. 87-95. Inst. Math. Statist. and Amer. Math. Soc., Providence, R.I. %H A103647 Yu. V. Prohorov, <a href="http://mi.mathnet.ru/eng/umn8214">Asymptotic behavior of the binomial distribution</a>, Uspekhi Mat. Nauk, 8:3(55) (1953), 135-142 (in Russian). See lambda1 in theorem 2 p. 137. %H A103647 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NormalDistribution.html">Normal Distribution</a>. %F A103647 Equals sqrt(2/Pi)*e^(-1/2). %e A103647 0.48394144903828669959566038587112130965734394147487005097511016856... %t A103647 RealDigits[ Sqrt[2/(E*Pi)], 10, 111][[1]] %Y A103647 Cf. A001113, A092605. %K A103647 cons,nonn %O A103647 0,1 %A A103647 _Robert G. Wilson v_, Feb 18 2005