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Decimal expansion of (1 + 4*e^(-3/2))/(3*sqrt(2*Pi)).
2

%I #30 Jun 24 2020 03:05:46

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

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

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

%N Decimal expansion of (1 + 4*e^(-3/2))/(3*sqrt(2*Pi)).

%C Occurs in a formula estimating the error in approximating a binomial distribution with a normal distribution. See [Prohorov].

%D 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 G. C. Greubel, <a href="/A238387/b238387.txt">Table of n, a(n) for n = 0..2500</a> [a(2500) corrected by _Georg Fischer_, Jun 23 2020]

%H 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 lambda2 in theorem 3 p. 137.

%e 0.25166883335507952210292348310539606239875418040734266550892142061...

%t RealDigits[N[(1 + 4*Exp[-3/2])/(3*Sqrt[2*Pi]), 1001]] (* _G. C. Greubel_, Jan 26 2016 *)

%o (PARI) (1 + 4*exp(-3/2))/(3*sqrt(2*Pi)) \\ _Michel Marcus_, Feb 27 2014

%Y Cf. A103647, A238388.

%K nonn,cons

%O 0,1

%A _Eric M. Schmidt_, Feb 26 2014