A203144 -id:A203144 - cp's OEIS frontend

A203142 Decimal expansion of Gamma(1/8).

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

Offset: 1

N. J. A. Sloane, Dec 29 2011

			7.5339415987976119046992298412151336246104195881490759409831...

G. C. Greubel, Table of n, a(n) for n = 1..5000
Raimundas Vidunas, Expressions for values of the Gamma function, arXiv:math/0403510 [math.CA], 2004.
Wikipedia, Particular values of the Gamma function: General rational arguments
Index to sequences related to the Gamma function

SetDefaultRealField(RealField(100)); Gamma(1/8); // G. C. Greubel, Mar 10 2018

RealDigits[Gamma[1/8], 10, 100][[1]] (* Bruno Berselli, Dec 13 2012 *)
RealDigits[Pi^(1/8) * 2^(17/8) * EllipticK[1/2]^(1/4) * EllipticK[3 - 2*Sqrt[2]]^(1/2), 10, 100][[1]] (* Vaclav Kotesovec, Apr 15 2024 *)

default(realprecision, 100); gamma(1/8) \\ G. C. Greubel, Jan 15 2017

this * A203144 * A231863 /2^(1/4) = A068466. - R. J. Mathar, Jan 15 2021

A203125 Decimal expansion of (1/8)! = Gamma(9/8).

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Dec 29 2011

			.94174269984970148808740373015189170307630244851863449262289...

Index to sequences related to the Gamma function

Cf. A068467, A202623, A203126, A203142.

RealDigits[(1/8)!,10,120][[1]] (* Harvey P. Dale, May 30 2014 *)

gamma(9/8) \\ Charles R Greathouse IV, Mar 25 2014

Equals A203142/8. - R. J. Mathar, Jan 15 2021
A203144 *this *A231863 *A011006 = A068467. - R. J. Mathar, Jan 15 2021
Equals Integral_{x=0..oo} exp(-x^8) dx. - Ilya Gutkovskiy, Sep 18 2021

A242011 Decimal expansion of sum_{k>=0} (-1)^k*(log(4k+1)/(4k+1)+log(4k+3)/(4k+3)).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Aug 11 2014

			0.02300458786273601031799260214514696231866764147508832909638...

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 8.

Cf. A203142, A203143, A203144, A203146.

s = (Pi/(2*Sqrt[2]))*(Log[Gamma[1/8]*Gamma[3/8]/(Gamma[5/8]*Gamma[7/8])] - (EulerGamma + Log[2*Pi])); Join[{0}, RealDigits[s, 10, 99] // First]

(Pi/(2*sqrt(3)))*(log(Gamma(1/8)/Gamma(3/8)/(Gamma(5/8)/Gamma(7/8))) - (gamma + log(2*Pi))), where gamma is Euler's constant and Gamma(x) is the Euler Gamma function.

A203128 Decimal expansion of (5/8)! = Gamma(13/8).

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Dec 29 2011

			.89657428005659798477251233716026446039512985762916708173167...

Index to sequences related to the Gamma function

RealDigits[(5/8)!,10,120][[1]] (* Harvey P. Dale, Jul 30 2019 *)

gamma(13/8) \\ Charles R Greathouse IV, Mar 25 2014

Equals 5*A203144/8. - R. J. Mathar, Jan 15 2021

Equals Integral_{x=0..oo} exp(-x^(8/5)) dx. - Ilya Gutkovskiy, Apr 10 2024

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A203142 Decimal expansion of Gamma(1/8).

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A203125 Decimal expansion of (1/8)! = Gamma(9/8).

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A242011 Decimal expansion of sum_{k>=0} (-1)^k*(log(4k+1)/(4k+1)+log(4k+3)/(4k+3)).

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A203128 Decimal expansion of (5/8)! = Gamma(13/8).

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