A114941 - OEIS

%I #13 Jul 19 2020 05:17:34

%S 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,

%T 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,

%U 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

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

%F From _Amiram Eldar_, Jul 19 2020: (Start)

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

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

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

%e 0.143835643791640325906...

%t 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 *)

%o (PARI) suminf(k=1, cos(k)/k!) \\ _Michel Marcus_, Jul 19 2020

%Y Cf. A001113, A049469, A049470, A114940.

%K cons,nonn

%O 0,2

%A _Stefan Steinerberger_, Feb 21 2006