A351400 -id:A351400 - cp's OEIS frontend

A099286 Decimal expansion of the error function at 1.

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

Offset: 0

Robert G. Wilson v, Oct 08 2004

			0.84270079294971486934122063508260925929606699796630290845993789783...

Eric Weisstein's World of Mathematics, Erf

Cf. A007680, A099287, A351400.

Mathematica
```
RealDigits[ Erf[1], 10, 105][[1]]
```
PARI
```
1 - erfc(1)
```

Equals 1-A099287.
Equals (1/e) Sum_{n >= 0} (1/(n/2)!) - 1. - Jean-François Alcover, Jun 14 2020
From Amiram Eldar, Jul 22 2020: (Start)
Equals (2/sqrt(Pi)) * Integral_{x=0..1} exp(-x^2) dx.
Equals (2/sqrt(Pi)) * Sum_{k>=0} (-1)^k/(k! * (2*k + 1)) = (2/sqrt(Pi)) * Sum_{k>=0} (-1)^k/A007680(k).
Equals (1/e) * Sum_{k>=1} 1/Gamma(k + 1/2). (End)

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

Original entry on oeis.org

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

Amiram Eldar, Feb 10 2022

The alternating sum of reciprocals of the factorials of the positive half-integers.

			0.60715770584139372911503823580074492116122092866515...

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).

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

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

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

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

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

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.

cp's OEIS Frontend

A099286 Decimal expansion of the error function at 1.

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