A099282 Decimal expansion of the cosine integral at 1.
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, 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, 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
Offset: 0
Examples
I=0.337403922900968134662646203889150769997578032585731894801318542...
Links
- Eric Weisstein's World of Mathematics, Cosine Integral.
Programs
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Mathematica
RealDigits[ CosIntegral[1], 10, 105][[1]]
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PARI
a = real(-eint1(I)) \\ Stanislav Sykora, May 08 2015
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PARI
-intnum(x=1,[oo,I],cos(x)/x) \\ Charles R Greathouse IV, May 08 2015
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)