A114941 Decimal expansion of the infinite sum Sum_{k>=1} cos(k)/k!.

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

Offset

0,2

Links

Table of n, a(n) for n=0..103.

Formula

From Amiram Eldar, Jul 19 2020: (Start)

Equals e^cos(1) * cos(sin(1)) - 1.

Equals cos(sin(1)) * (cosh(cos(1)) + sinh(cos(1))) - 1.

Equals (e^(e^i) + e^(e^(-i)))/2 - 1. (End)

Example

0.143835643791640325906...

Mathematica

RealDigits[Sum[N[Cos[i], 400]/i!, {i, 1, 300}]][[1]] (*which is accurate to 300 digits*) (* corrected by Harvey P. Dale, Nov 29 2011 *)

Prog

(PARI) suminf(k=1, cos(k)/k!) \\ Michel Marcus, Jul 19 2020

Crossrefs

Cf. A001113, A049469, A049470, A114940.

Sequence in context: A231892 A065628 A077589 * A161016 A019835 A200345

Adjacent sequences: A114938 A114939 A114940 * A114942 A114943 A114944

Keyword

cons,nonn

Author

Stefan Steinerberger, Feb 21 2006

Status

approved