A147709 -id:A147709 - cp's OEIS frontend

A147708 Decimal expansion of cosh(EulerGamma).

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

Offset: 1

Artur Jasinski, Nov 11 2008

			1.171265950778541577530323658949030167967677800614291686755912...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A001620, A098907.

Cf. A147709 (with sinh), A147710 (with tanh), A147711 (with coth).

SetDefaultRealField(RealField(100)); R:= RealField(); Cosh(EulerGamma(R)); // G. C. Greubel, Aug 29 2018

First[RealDigits[N[(Exp[EulerGamma] + Exp[ -EulerGamma])/2, 100]]]

default(realprecision, 100); cosh(Euler) \\ G. C. Greubel, Aug 29 2018

A147710 Decimal expansion of tanh(EulerGamma).

Original entry on oeis.org

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

Offset: 0

Artur Jasinski, Nov 11 2008

			0.52063877277941655882939459166902813428767319381048760826540...

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

Cf. A001620, A098907.

Cf. A147708 (with cosh), A147709 (with sinh), A147711 (with coth).

SetDefaultRealField(RealField(100)); R:= RealField(); Tanh(EulerGamma(R)); // G. C. Greubel, Aug 29 2018

First[RealDigits[N[(Exp[EulerGamma] - Exp[ -EulerGamma])/(Exp[EulerGamma] + Exp[ -EulerGamma]), 100]]]
RealDigits[Tanh[EulerGamma],10,120][[1]] (* Harvey P. Dale, Aug 10 2020 *)

default(realprecision, 100); tanh(Euler) \\ G. C. Greubel, Aug 29 2018

Leading zero removed and offset adjusted by R. J. Mathar, Feb 05 2009

A147711 Decimal expansion of coth(EulerGamma).

Original entry on oeis.org

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

Offset: 1

Artur Jasinski, Nov 11 2008

			1.920717496051102737973648663483211255479106194024976155441...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A001620, A098907.

Cf. A147708 (with cosh), A147709 (with sinh), A147710 (with tanh).

SetDefaultRealField(RealField(100)); R:= RealField(); (Exp(EulerGamma(R)) + Exp(-EulerGamma(R)))/(Exp(EulerGamma(R)) - Exp(-EulerGamma(R))); // G. C. Greubel, Aug 29 2018

First[RealDigits[N[(Exp[EulerGamma] + Exp[ -EulerGamma])/(Exp[EulerGamma] - Exp[ -EulerGamma]), 100]]]

default(realprecision, 100); (exp(Euler) + exp(-Euler))/(exp(Euler) - exp(-Euler)) \\ G. C. Greubel, Aug 29 2018

1/tanh(Euler) \\ Charles R Greathouse IV, May 14 2019

A322603 Continued fraction for sinh(gamma).

Original entry on oeis.org

0, 1, 1, 1, 1, 3, 2, 11, 2, 1, 2, 3, 1, 8, 1, 1, 2, 3, 2, 8, 1, 3, 5, 17, 15, 2, 1, 1, 1, 1, 2, 7, 1, 1, 1, 4, 1, 11, 1, 2, 20, 19, 6, 7, 23, 14, 1, 10, 3, 2, 1, 1, 154, 5, 6, 2, 2, 1, 23, 1, 1, 28, 2, 2, 5, 2, 1, 1, 1, 1332, 1, 15, 1, 1, 1, 1, 1, 1, 2, 6, 2, 1, 2, 1, 4, 5, 28, 6, 1

Offset: 0

Tristan Cam, Dec 20 2018

Continued fraction of (exp(gamma)-exp(-gamma))/2 = sinh(gamma) (A147709), where gamma is the Euler-Mascheroni constant (A001620).

See A322602 for the continued fraction of cosh(gamma).

			0 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(3 + 1/(2 + 1/(11 + ...))))))) = 0.60980646721165640770618044...

Cf. A147709 (decimal expansion), A001620 (Euler-Mascheroni constant), A322602.

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

ContinuedFraction[ (Exp[EulerGamma] - Exp[ -EulerGamma])/2, 100]

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

Offset changed and data corrected by Andrew Howroyd, Jul 05 2024

cp's OEIS Frontend

A147708 Decimal expansion of cosh(EulerGamma).

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A147710 Decimal expansion of tanh(EulerGamma).

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A147711 Decimal expansion of coth(EulerGamma).

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Magma

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A322603 Continued fraction for sinh(gamma).

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Maple

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