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A190732
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Decimal expansion of 2/sqrt(Pi).
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8
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1, 1, 2, 8, 3, 7, 9, 1, 6, 7, 0, 9, 5, 5, 1, 2, 5, 7, 3, 8, 9, 6, 1, 5, 8, 9, 0, 3, 1, 2, 1, 5, 4, 5, 1, 7, 1, 6, 8, 8, 1, 0, 1, 2, 5, 8, 6, 5, 7, 9, 9, 7, 7, 1, 3, 6, 8, 8, 1, 7, 1, 4, 4, 3, 4, 2, 1, 2, 8, 4, 9, 3, 6, 8, 8, 2
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OFFSET
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1,3
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COMMENTS
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According to Weisstein, some mathematicians define erf(z) without reference to this constant.
Also equals the average absolute value of the difference of two independent normally distributed random numbers with mean 0 and variance 1. - Jean-François Alcover, Oct 31 2014
Limit_{n->infinity} (2^(1 - 2 n^2) n binomial(2 n^2, n^2) is proper to compute this constant (and also Pi) in a base of power 2. - Ralf Steiner, Apr 23 2017
A gauge point marked "c" on slide rule calculating devices in the 20th century. The Pickworth reference notes its use "in calculating the contents of cylinders". - Peter Munn, Aug 14 2020
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REFERENCES
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Chi Keung Cheung et al., Getting Started with Mathematica, 2nd Ed. New York: J. Wiley (2005) p. 79.
C. N. Pickworth, The Slide Rule, 24th Ed., Pitman, London (1945), p 53, Gauge Points.
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LINKS
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Eric Weisstein's World of Mathematics, Erf
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FORMULA
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EXAMPLE
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1.12837916709551257...
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MATHEMATICA
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RealDigits[2/Sqrt[Pi], 10, 100][[1]]
RealDigits[Limit[2^(1 - 2 m^2) m Binomial[2 m^2, m^2], m -> Infinity], 10, 100][[1]] (* Ralf Steiner, Apr 22 2017 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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