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Search: id:A103647
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| A103647 |
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Decimal expansion of area of the largest rectangle under the normal curve. |
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+0
1
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| 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; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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The normal curve is 'nc' = 1/(sqrt(2Pi)*E^(1/2*x^-x). Area = 2*x*nc. d(Area) = (sqrt(2/Pi) - sqrt(2/Pi)*x^2)*e^(1/2*x^-2). Maximum at x = +/- 1.
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REFERENCES
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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.
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LINKS
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Eric Weisstein's World of Mathematics, Normal Distribution.
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FORMULA
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sqrt(2/Pi)*e^(-1/2).
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EXAMPLE
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0.48394144903828669959566038587112130965734394147487005097511016856...
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MATHEMATICA
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RealDigits[ Sqrt[2/Pi]E^(-1/2), 10, 111][[1]]
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CROSSREFS
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Cf. A001113, A092605.
Adjacent sequences: A103644 A103645 A103646 this_sequence A103648 A103649 A103650
Sequence in context: A065191 A021678 A066199 this_sequence A033197 A124002 A014457
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KEYWORD
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cons,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 18 2005
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