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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
Eric Weisstein's World of Mathematics, Erf.
Eric Weisstein's World of Mathematics, 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
Sequence in context: A341303 A011148 A365307 * A176020 A048650 A125313
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.)