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A175379 Decimal expansion of Gamma(1/6). 8
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(Gamma(i/n), i=1..n-1) = 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

Table of n, a(n) for n=1..105.

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

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.

Wikipedia, Particular values of the Gamma function: General rational arguments

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

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. A002161, A073005, A073006, A203145.

Sequence in context: A161981 A091284 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 October 25 11:39 EDT 2014. Contains 248527 sequences.