login
A114940
Decimal expansion of the infinite sum Sum_{k>=1} sin(k)/k!.
2
1, 2, 7, 9, 8, 8, 3, 0, 0, 1, 3, 7, 3, 0, 2, 2, 4, 9, 3, 9, 0, 8, 4, 6, 2, 3, 0, 1, 2, 0, 1, 3, 9, 1, 8, 8, 8, 2, 3, 5, 6, 3, 8, 9, 0, 7, 7, 3, 9, 0, 2, 8, 8, 1, 1, 4, 7, 2, 3, 8, 8, 2, 1, 5, 8, 0, 5, 3, 7, 3, 7, 1, 7, 8, 9, 6, 8, 4, 5, 4, 0, 1, 2, 1, 5, 4, 6, 4, 0, 4, 9, 2, 5, 6, 1, 2, 6, 5, 9, 1, 5, 3, 7, 3, 7, 4
OFFSET
1,2
COMMENTS
This is the imaginary part of exp(exp(i)), i the imaginary unit, where the real part is 1+A114941. - R. J. Mathar, Apr 11 2024
FORMULA
From Amiram Eldar, Jul 19 2020: (Start)
Equals e^cos(1) * sin(sin(1)).
Equals sin(sin(1)) * (cosh(cos(1)) + sinh(cos(1))).
Equals (-i)*(e^(e^i) - e^(e^(-i)))/2. (End)
EXAMPLE
1.279883001373022493908...
MATHEMATICA
Sum[N[Sin[i], 400]/i!, {i, 1, 300}] (which is accurate to 300 digits).
PROG
(PARI) suminf(k=1, sin(k)/k!) \\ Michel Marcus, Jul 19 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved