A346440 Decimal expansion of the constant Sum_{k>=0} (-1)^k/(4*k)!.

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

Offset: 0

Author

Sean A. Irvine, Jul 17 2021

Keywords

• cons
• nonn

Examples

			0.95835813283300701621040446...
		

Links

• Michael I. Shamos, A catalog of the real numbers (2011).

Crossrefs

Cf. A068985, A049470, A346441, A346439, A346438, A346437, A346436, A346435, A196498.

Programs

Mathematica

RealDigits[Sum[(-1)^k/(4*k)!, {k, 0, Infinity}], 10, 100][[1]] (* Amiram Eldar, Jul 18 2021 *)

PARI

sumalt(k=0, (-1)^k/(4*k)!) \\ Michel Marcus, Jul 18 2021

Formula

Equals cos(sqrt(2)/2)*cosh(sqrt(2)/2). - Amiram Eldar, Jul 18 2021

Continued fraction: 1/(1 + 1/(23 + 24/(1679 + ... + P(n-1)/((P(n) - 1) + ... )))), where P(n) = (4*n)*(4*n - 1)*(4*n - 2)*(4*n - 3) for n >= 1. Cf. A346441. - Peter Bala, Feb 21 2024