A306858 Decimal expansion of 1 - 1/(1*3) + 1/(1*3*5) - 1/(1*3*5*7) + ...

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

Offset: 0

Author

Ilya Gutkovskiy, Jun 24 2019

Keywords

• nonn
• cons

Examples

			0.7247784590070763318182279676062161663121329...
		

Crossrefs

Cf. A001147, A014481, A060196, A068996, A092605, A113014.

Programs

Mathematica

RealDigits[Sqrt[Pi/(2 Exp[1])] Erfi[1/Sqrt[2]], 10, 110] [[1]]
RealDigits[Sqrt[2] DawsonF[1/Sqrt[2]], 10, 110] [[1]]

Formula

Equals sqrt(Pi/(2*exp(1)))*erfi(1/sqrt(2)), where erfi is the imaginary error function.

Equals (1/sqrt(e)) * Sum_{k>=0} 1/(2^k * k! * (2*k+1)) = 1/(sqrt(e)) * Sum_{k>=0} 1/A014481(k). - Amiram Eldar, Nov 12 2021

Equals 1/(1+A113014). - Jon Maiga, Nov 12 2021