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 A322712 Decimal expansion of Sum_{k = -infinity .. infinity} exp(-k^2/4) - Integral_{x = -infinity .. infinity} exp(-x^2/4) dx. 0
 5, 0, 7, 4, 2, 9, 8, 4, 5, 8, 4, 5, 7, 9, 5, 6, 9, 8, 0, 8, 8, 0, 5, 7, 0, 9, 4, 8, 3, 4, 2, 0, 1, 2, 0, 4, 5, 5, 1, 7, 9, 0, 8, 0, 3, 4, 5, 1, 5, 9, 0, 0, 4, 1, 2, 9, 9, 9, 9, 4, 0, 6, 0, 9, 2, 0, 9, 3, 2, 2, 5, 5, 3, 1, 1, 0, 8, 1, 0, 6, 4, 4, 5, 3, 7, 0, 5 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET -16,1 COMMENTS This constant is the small difference between the sum and integral of the same function. The integral is 3.54490770181103205... (10 * sqrt(Pi)/5, see A019707) and the sum agrees up to 15 decimal digits, 3.54490770181103210... This approximation is similar to exact identities of sum and integral of the same function known as "Sophomore's dream" (A073009, A083648). LINKS Nick Lord, Solution to problem 81.F, The Mathematical Gazette, Vol. 82, No. 493 (1998), pp. 130-131. T. J. Osier, Get billions and billions of correct digits of pi from a wrong formula, Mathematics and Computer Education, Vol. 33 (1999), pp. 40-45. FORMULA Equals 2 * sqrt(4*Pi) * Sum_{k >= 1} exp(-4 * Pi^2 * k^2) ~ 2 * sqrt(4*Pi) * exp(-4*Pi^2). EXAMPLE 5.0742984584579569808805709483420120455179080345159... * 10^(-17). MATHEMATICA s = Sum[Exp[-n^2/4], {n, -Infinity, Infinity}] - Sqrt[4 * Pi]; RealDigits[s, 10, 100][[1]] PROG (PARI) default(realprecision, 100); 2*sqrt(4*Pi)*suminf(k=1, exp(-4*Pi^2*k^2)) \\ Michel Marcus, Dec 25 2018 CROSSREFS Cf. A019707, A073009, A083648. Sequence in context: A201656 A168195 A333507 * A244345 A021873 A020801 Adjacent sequences:  A322709 A322710 A322711 * A322713 A322714 A322715 KEYWORD nonn,cons AUTHOR Amiram Eldar, Dec 24 2018 STATUS approved

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Last modified June 4 16:06 EDT 2020. Contains 334828 sequences. (Running on oeis4.)