A351400 - OEIS

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

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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