A351401 Decimal expansion of erfi(1)/e, where erfi is the imaginary error function.

6, 0, 7, 1, 5, 7, 7, 0, 5, 8, 4, 1, 3, 9, 3, 7, 2, 9, 1, 1, 5, 0, 3, 8, 2, 3, 5, 8, 0, 0, 7, 4, 4, 9, 2, 1, 1, 6, 1, 2, 2, 0, 9, 2, 8, 6, 6, 5, 1, 5, 6, 9, 1, 5, 9, 1, 6, 9, 4, 4, 1, 9, 1, 9, 2, 7, 2, 0, 8, 7, 6, 9, 4, 9, 2, 0, 2, 8, 1, 1, 8, 2, 0, 1, 6, 3, 9, 1, 3, 1, 6, 5, 2, 6, 3, 3, 2, 6, 8, 5, 4, 8, 1, 0, 4

Offset

0,1

Comments

The alternating 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. (4.12.9.6).

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=0..104.

Eric Weisstein's World of Mathematics, Erfi.

Eric Weisstein's World of Mathematics, Mittag-Leffler Function.

Wikipedia, Mittag-Leffler function.

Formula

Equals Sum_{k>=0} (-1)^k/(k + 1/2)! = Sum_{k>=1} (-1)^(k+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)!!.

Equals A068985 * A099288.

Example

0.60715770584139372911503823580074492116122092866515...

Maple

evalf(exp(-1)*erfi(1), 120);  # Alois P. Heinz, Feb 10 2022

Mathematica

RealDigits[Erfi[1]/E, 10, 100][[1]]

Prog

(PARI) real(-I*(1.0-erfc(I)))/exp(1) \\ Michel Marcus, Feb 10 2022

Crossrefs

Cf. A001113, A001147, A068985, A087197, A099288, A122803, A351400.

Sequence in context: A222608 A353091 A021900 * A273413 A341906 A365163

Adjacent sequences: A351398 A351399 A351400 * A351402 A351403 A351404

Keyword

nonn,cons

Author

Amiram Eldar, Feb 10 2022

Status

approved