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

Offset: 1

Author

R. J. Mathar, Apr 24 2010

Keywords

• cons
• nonn

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

Examples

			Equals 5.56631600178023...
		

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

Crossrefs

Cf. A073006, A203145.

Programs

Magma

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

Maple

evalf(GAMMA(1/6)) ;

Mathematica

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

PARI

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

Formula

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