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A175379 Decimal expansion of Gamma(1/6). 22
5, 5, 6, 6, 3, 1, 6, 0, 0, 1, 7, 8, 0, 2, 3, 5, 2, 0, 4, 2, 5, 0, 0, 9, 6, 8, 9, 5, 2, 0, 7, 7, 2, 6, 1, 1, 1, 3, 9, 8, 7, 9, 9, 1, 1, 4, 8, 7, 2, 8, 5, 3, 4, 6, 1, 6, 1, 6, 7, 4, 4, 6, 2, 6, 3, 2, 2, 9, 0, 7, 5, 0, 2, 8, 1, 7, 8, 0, 2, 3, 0, 5, 5, 0, 3, 3, 8, 9, 6, 5, 3, 6, 2, 1, 0, 2, 1, 7, 5, 4, 6, 5, 9, 8, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A175379 * A073005 * A002161 * A073006 * A203145 = 4*sqrt(Pi^5/3), which is the case n=6 of Product_{i=1..n-1} Gamma(i/n) = sqrt((2*Pi)^(n-1)/n). - Bruno Berselli, Dec 18 2012

The transcendence of this constant is in the mathematical folklore; see Finch (who credits Nesterenko) and Gun-Murty-Rath. - Charles R Greathouse IV, Nov 11 2013

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

Steven Finch, Errata and addenda to Mathematical Constants (2013)

Steven R. Finch, Errata and Addenda to Mathematical Constants, Jan 22 2016. [Cached copy, with permission of the author]

Sanoli Gun, M. Ram Murty, and Purusottam Rath, Transcendence of the log gamma function and some discrete periods, J. Number Theory (2009), doi:10.1016/j.jnt.2009.01.008

R. 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 entries for transcendental numbers

FORMULA

Equals 2*Pi/A203145 = A002194 * A073005^2 / (A002161 * A002580) = A019692 / 1.12878703....

EXAMPLE

Equals 5.56631600178023...

MAPLE

evalf(GAMMA(1/6)) ;

MATHEMATICA

RealDigits[Gamma[1/6], 10, 110][[1]] (* Bruno Berselli, Dec 13 2012 *)

PROG

(PARI) gamma(1/6) \\ Charles R Greathouse IV, Nov 16 2013

(MAGMA) SetDefaultRealField(RealField(100)); Gamma(1/6); // G. C. Greubel, Mar 10 2018

CROSSREFS

Cf. decimal expansions of Gamma(1/k): A002161 (k=2), A073005 (k=3), A068466 (k=4), A175380 (k=5), A220086 (k=7), A203142 (k=8), A203140 (k=12), A203139 (k=16), A203138 (k=24), A203137 (k=48).

Cf. A073006, A203145.

Sequence in context: A091284 A276860 A046604 * A106746 A152481 A157276

Adjacent sequences:  A175376 A175377 A175378 * A175380 A175381 A175382

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Apr 24 2010

STATUS

approved

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Last modified November 17 13:32 EST 2019. Contains 329230 sequences. (Running on oeis4.)