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A103647
Decimal expansion of area of the largest rectangle under the normal curve.
2
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, 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, 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
OFFSET
0,1
COMMENTS
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.
Occurs in a formula estimating the error in approximating a binomial distribution with a Poisson distribution. See [Prohorov]. - Eric M. Schmidt, Feb 26 2014
REFERENCES
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.
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.
LINKS
Yu. V. Prohorov, Asymptotic behavior of the binomial distribution, Uspekhi Mat. Nauk, 8:3(55) (1953), 135-142 (in Russian). See lambda1 in theorem 2 p. 137.
Eric Weisstein's World of Mathematics, Normal Distribution.
FORMULA
Equals sqrt(2/Pi)*e^(-1/2).
EXAMPLE
0.48394144903828669959566038587112130965734394147487005097511016856...
MATHEMATICA
RealDigits[ Sqrt[2/(E*Pi)], 10, 111][[1]]
CROSSREFS
Sequence in context: A021678 A180594 A066199 * A372356 A033197 A124002
KEYWORD
cons,nonn
AUTHOR
Robert G. Wilson v, Feb 18 2005
STATUS
approved