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

0,1

Links

Table of n, a(n) for n=0..104.

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

Cf. A001620, A099281, A257535.

Sequence in context: A324548 A249383 A187419 * A002937 A085870 A336510

Adjacent sequences: A099279 A099280 A099281 * A099283 A099284 A099285

Keyword

cons,nonn

Author

Robert G. Wilson v, Oct 08 2004

Status

approved