A119806 -id:A119806 - cp's OEIS frontend

A119807 Decimal expansion of sin(gamma).

5, 4, 5, 6, 9, 2, 8, 2, 3, 2, 0, 3, 9, 9, 2, 7, 8, 8, 1, 5, 7, 3, 5, 6, 5, 0, 0, 1, 6, 1, 4, 3, 0, 7, 4, 3, 5, 0, 3, 7, 8, 8, 1, 0, 9, 2, 0, 5, 2, 2, 0, 7, 1, 1, 1, 5, 1, 9, 1, 4, 1, 5, 2, 6, 8, 9, 7, 8, 3, 0, 5, 3, 7, 9, 0, 2, 8, 3, 1, 9, 1, 0, 5, 7, 5, 5, 9, 6, 1, 5, 4, 7, 9, 2, 3, 7, 4, 6, 1, 2, 1, 0, 6, 0, 8

Offset: 0

T. D. Noe, May 24 2006

This is the imaginary part of exp(i*gamma), where gamma is the Euler-Mascheroni constant A001620. See A119806 for the real part. The constant exp(gamma) (A073004) appears in many formulas. Does exp(i*gamma)?

			0.54569282320399278815735650016143074350378810920522...

G. C. Greubel, Table of n, a(n) for n = 0..10000

SetDefaultRealField(RealField(100)); R:= RealField(); Sin(EulerGamma(R)); // G. C. Greubel, Aug 30 2018

Mathematica
```
RealDigits[Sin[EulerGamma],10,150][[1]]
```

default(realprecision, 100); sin(Euler) \\ G. C. Greubel, Aug 30 2018

A322545 Continued fraction for cos(gamma).

Original entry on oeis.org

0, 1, 5, 5, 1, 4, 8, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 18, 1, 73, 2, 5, 3, 5, 4, 1, 1, 1, 7, 1, 4, 2, 1, 1, 32, 12, 2, 19, 8, 1, 1, 1, 1, 1, 3, 5, 2, 70, 1, 6, 6, 1, 52, 2, 1, 2, 10, 1, 1, 1, 4, 1, 3, 1, 5, 1, 7, 3, 1, 1, 1, 20, 5, 6, 6, 2, 4, 3, 7, 1, 1, 2, 10, 1, 9, 12, 45, 1, 16, 2

Offset: 0

Tristan Cam, Dec 20 2018

Continued fraction of the real part of exp(i*gamma) = cos(gamma) (A119806), where gamma is the Euler-Mascheroni constant (A001620).

See A322601 for the continued fraction of imaginary part.

			0 + 1/(1 + 1/(5 + 1/(5 + 1/(1 + 1/(4 + 1/(8 + 1/(1 + ...))))))) = 0.8379852878801965399549928...

Cf. A119806 (decimal expansion), A001620 (Euler-Mascheroni constant), A322601.

with(numtheory): cfrac(cos(gamma),100,'quotients'); # Muniru A Asiru, Dec 20 2018

ContinuedFraction[ Cos[EulerGamma], 100]

contfrac(cos(Euler)) \\ Michel Marcus, Dec 21 2018

Offset changed by Andrew Howroyd, Jul 07 2024

cp's OEIS Frontend

A119807 Decimal expansion of sin(gamma).

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