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
KEYWORD
cons,nonn
AUTHOR
Robert G. Wilson v, Feb 18 2005
STATUS
approved