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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 (list; constant; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..104.

Yu. V. Prohorov, Asymptotic behavior of the binomial distribution, Uspekhi Mat. Nauk, 8:3(55) (1953), 135-142 (in Russian).

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

Cf. A001113, A092605.

Sequence in context: A021678 A180594 A066199 * A033197 A124002 A014457

Adjacent sequences:  A103644 A103645 A103646 * A103648 A103649 A103650

KEYWORD

cons,nonn

AUTHOR

Robert G. Wilson v, Feb 18 2005

STATUS

approved

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Last modified May 26 00:32 EDT 2020. Contains 334613 sequences. (Running on oeis4.)