A367549 Decimal expansion of 1 - DawsonF(1/2).

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

Offset: 0

Author

Peter Luschny, Nov 23 2023

Keywords

• nonn
• cons

Examples

			0.57556361649797770406595764751033042890357052264030796184866030336675484524040...
		

Links

• Eric Weisstein's World of Mathematics, Dawson's Integral.

Crossrefs

Cf. A019704, A092042, A367563.

Programs

Maple

1 - sqrt(Pi/4)*erfi(1/2)/exp(1/4): evalf(%, 109);

Mathematica

N[1 - DawsonF[1/2], 110] // RealDigits // First

Formula

Equals 1 - sqrt(Pi/4) * erfi(1/2) / exp(1/4) = 1 - A019704 * A367563 / A092042.

Let C denote the constant. Then:

2*C - 1 = Sum_{n>=0} (-1)^n / Pochhammer(n, n).

2*(C - 1) = Sum_{n>=1} (-1)^n*Gamma(n) / Gamma(2*n).

Equals Integral_{x=0..oo} exp(-x)*cos(sqrt(x)) dx. - Kritsada Moomuang, Jun 06 2025