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 A351400 Decimal expansion of e * erf(1), where erf is the error function. 1
 2, 2, 9, 0, 6, 9, 8, 2, 5, 2, 3, 0, 3, 2, 3, 8, 2, 3, 0, 9, 4, 9, 5, 3, 7, 1, 2, 6, 8, 6, 2, 1, 4, 7, 3, 1, 6, 9, 3, 7, 0, 8, 7, 5, 9, 0, 5, 3, 5, 7, 0, 6, 9, 1, 1, 2, 2, 1, 4, 2, 7, 8, 5, 6, 9, 8, 3, 5, 7, 1, 2, 0, 8, 5, 3, 3, 3, 0, 4, 3, 4, 9, 3, 6, 4, 3, 3, 4, 0, 8, 5, 8, 0, 5, 7, 7, 9, 8, 9, 4, 9, 4, 6, 1, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sum of reciprocals of the factorials of the positive half-integers. REFERENCES Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, and Sergei Rogosin, Mittag-Leffler Functions, Related Topics and Applications, New York, NY: Springer, 2020. See p. 94, eq. (4.12.9.5). Constantin Milici, Gheorghe Drăgănescu, and J. Tenreiro Machado, Fractional Differential Equations, Introduction to Fractional Differential Equations, Springer, Cham, 2019. See p. 12, eq. (1.9). LINKS Table of n, a(n) for n=1..105. Eric Weisstein's World of Mathematics, Erf. Eric Weisstein's World of Mathematics, Mittag-Leffler Function. Wikipedia, Mittag-Leffler function. FORMULA Equals Sum_{k>=0} 1/(k + 1/2)! = Sum_{k>=1} 1/Gamma(k + 1/2). Equals E_{1, 3/2}(1), where E_{a,b}(z) is the two-parameter Mittag-Leffler function. Equals (1/sqrt(Pi)) * Sum_{k>=1) 2^k/(2*k-1)!! = (1/sqrt(Pi)) * Sum_{k>=1) A000079(k)/A001147(k). Equals A001113 * A099286. Equals A087197 * A125961. EXAMPLE 2.29069825230323823094953712686214731693708759053570... MAPLE evalf(exp(1)*erf(1), 120); # Alois P. Heinz, Feb 10 2022 MATHEMATICA RealDigits[E * Erf[1], 10, 100][[1]] PROG (PARI) exp(1)*(1 - erfc(1)) \\ Michel Marcus, Feb 10 2022 CROSSREFS Cf. A000079, A001113, A001147, A087197, A099286, A125961, A351401. Sequence in context: A341303 A011148 A365307 * A176020 A048650 A125313 Adjacent sequences: A351397 A351398 A351399 * A351401 A351402 A351403 KEYWORD nonn,cons AUTHOR Amiram Eldar, Feb 10 2022 STATUS approved

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Last modified April 18 22:18 EDT 2024. Contains 371782 sequences. (Running on oeis4.)