cp's OEIS Frontend

A099282 Decimal expansion of the cosine integral at 1.

%I A099282 #18 Feb 16 2025 08:32:54
%S A099282 3,3,7,4,0,3,9,2,2,9,0,0,9,6,8,1,3,4,6,6,2,6,4,6,2,0,3,8,8,9,1,5,0,7,
%T A099282 6,9,9,9,7,5,7,8,0,3,2,5,8,5,7,3,1,8,9,4,8,0,1,3,1,8,5,4,2,4,3,6,1,3,
%U A099282 0,3,3,0,0,2,5,0,5,6,0,5,2,8,9,6,8,4,8,1,8,3,0,9,7,3,2,2,9,9,4,6,0,4,9,4,8
%N A099282 Decimal expansion of the cosine integral at 1.
%H A099282 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CosineIntegral.html">Cosine Integral</a>.
%F A099282 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
%F A099282 From _Amiram Eldar_, Jun 25 2021: (Start)
%F A099282 Equals -Integral_{x>=1} cos(x)/x dx.
%F A099282 Equals gamma - Integral_{x=0..1} (1-cos(x))/x dx, where gamma = A001620.
%F A099282 Equals gamma + Sum_{k>=1} (-1)^k/((2*k)*(2*k)!). (End)
%e A099282 I=0.337403922900968134662646203889150769997578032585731894801318542...
%t A099282 RealDigits[ CosIntegral[1], 10, 105][[1]]
%o A099282 (PARI) a = real(-eint1(I)) \\ _Stanislav Sykora_, May 08 2015
%o A099282 (PARI) -intnum(x=1,[oo,I],cos(x)/x) \\ _Charles R Greathouse IV_, May 08 2015
%Y A099282 Cf. A001620, A099281, A257535.
%K A099282 cons,nonn
%O A099282 0,1
%A A099282 _Robert G. Wilson v_, Oct 08 2004