OFFSET
0,1
LINKS
Eric Weisstein's World of Mathematics, Cosine Integral.
FORMULA
Equals -real(E_1(I)) = -(E_1(I)+E_1(-I))/2, where E_1(z) = Integral_{t>=1} exp(-t*z)/t dt is the exponential integral. - Stanislav Sykora, May 08 2015
From Amiram Eldar, Jun 25 2021: (Start)
Equals -Integral_{x>=1} cos(x)/x dx.
Equals gamma - Integral_{x=0..1} (1-cos(x))/x dx, where gamma = A001620.
Equals gamma + Sum_{k>=1} (-1)^k/((2*k)*(2*k)!). (End)
EXAMPLE
I=0.337403922900968134662646203889150769997578032585731894801318542...
MATHEMATICA
RealDigits[ CosIntegral[1], 10, 105][[1]]
PROG
(PARI) a = real(-eint1(I)) \\ Stanislav Sykora, May 08 2015
(PARI) -intnum(x=1, [oo, I], cos(x)/x) \\ Charles R Greathouse IV, May 08 2015
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Robert G. Wilson v, Oct 08 2004
STATUS
approved