login
Decimal expansion of x^(1/3) * y^(2/3), where x is the constant in A103647 and y is the constant in A238387.
1

%I #13 Jun 24 2020 05:26:51

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

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

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

%N Decimal expansion of x^(1/3) * y^(2/3), where x is the constant in A103647 and y is the constant in A238387.

%C Occurs in a formula concerning the error in various approximations of binomial distributions. 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 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 lambda p. 136.

%e 0.31295644329257221613608878676292116801179369870970508298082007371...

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

%Y Cf. A103647, A238387.

%K nonn,cons

%O 0,1

%A _Eric M. Schmidt_, Feb 26 2014