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A068466 Decimal expansion of Gamma(1/4). 37
3, 6, 2, 5, 6, 0, 9, 9, 0, 8, 2, 2, 1, 9, 0, 8, 3, 1, 1, 9, 3, 0, 6, 8, 5, 1, 5, 5, 8, 6, 7, 6, 7, 2, 0, 0, 2, 9, 9, 5, 1, 6, 7, 6, 8, 2, 8, 8, 0, 0, 6, 5, 4, 6, 7, 4, 3, 3, 3, 7, 7, 9, 9, 9, 5, 6, 9, 9, 1, 9, 2, 4, 3, 5, 3, 8, 7, 2, 9, 1, 2, 1, 6, 1, 8, 3, 6, 0, 1, 3, 6, 7, 2, 3, 3, 8, 4, 3, 0, 0, 3, 6, 1, 4, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Nesterenko proves that this constant is transcendental (he cites Chudnovsky as the first to show this); in fact it is algebraically independent of Pi and e^Pi over Q. - Charles R Greathouse IV, Nov 11 2013
LINKS
William Duke and Özlem Imamoḡlu, Special values of multiple gamma functions, Journal de théorie des nombres de Bordeaux, Vol. 18. No. 1 (2006), pp. 113-123.
Greg J. Fee and Simon Plouffe, Gamma(1/4) to 25000 digits.
Yu. V. Nesterenko, Modular functions and transcendence questions, Sbornik: Mathematics, Vol. 187, No. 9 (1996), pp. 1319-1348. (English translation)
Simon Plouffe, GAMMA(1/4) to 512 digits.
Dan Romik, On Viazovska's modular form inequalities, arXiv:2303.13427 [math.NT], 2023.
Eric Weisstein's World of Mathematics, Gamma Function.
FORMULA
From Amiram Eldar, Jun 12 2021: (Start)
Equals sqrt(2*sqrt(2*Pi^3)*G), where G is Gauss's constant (A014549).
Equals (2*Pi)^(3/4) * Product_{k>=1} tanh(k*Pi/2) (Duke and Imamoḡlu, 2006). (End)
EXAMPLE
3.6256099082219083119306851558676720029951676828800654674333...
MAPLE
evalf(GAMMA(1/4));
MATHEMATICA
RealDigits[Gamma[1/4], 10, 110][[1]] (* Bruno Berselli, Dec 13 2012 *)
PROG
(PARI) default(realprecision, 1080); x=gamma(1/4); for (n=1, 1000, d=floor(x); x=(x-d)*10; write("b068466.txt", n, " ", d)); \\ Harry J. Smith, Apr 19 2009
(Magma) R:= RealField(100); SetDefaultRealField(R); Gamma(1/4); // G. C. Greubel, Mar 10 2018
CROSSREFS
Sequence in context: A319513 A160590 A111952 * A194076 A194040 A194065
KEYWORD
cons,easy,nonn
AUTHOR
Benoit Cloitre, Mar 10 2002
STATUS
approved

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Last modified March 19 07:41 EDT 2024. Contains 370958 sequences. (Running on oeis4.)