A351400 Decimal expansion of e * erf(1), where erf is the error function.

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

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: A379577 A011148 A365307 * A176020 A048650 A125313

Adjacent sequences: A351397 A351398 A351399 * A351401 A351402 A351403

Keyword

nonn,cons

Author

Amiram Eldar, Feb 10 2022

Status

approved