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A068466
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Decimal expansion of Gamma(1/4).
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37
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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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)
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EXAMPLE
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3.6256099082219083119306851558676720029951676828800654674333...
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MAPLE
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evalf(GAMMA(1/4));
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MATHEMATICA
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RealDigits[Gamma[1/4], 10, 110][[1]] (* Bruno Berselli, Dec 13 2012 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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