A175379 - OEIS

A175379

Decimal expansion of Gamma(1/6).

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

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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)

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

Index entries to sequences related to the Gamma function

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 *)