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A220086 Decimal expansion of Gamma(1/7). 23

%I

%S 6,5,4,8,0,6,2,9,4,0,2,4,7,8,2,4,4,3,7,7,1,4,0,9,3,3,4,9,4,2,8,9,9,6,

%T 2,6,2,6,2,1,1,3,5,1,8,7,3,8,4,1,3,5,1,4,8,9,4,0,1,6,8,8,1,9,1,4,8,5,

%U 7,6,2,0,4,7,3,8,2,3,9,1,3,7,7,9,0,5,6

%N Decimal expansion of Gamma(1/7).

%C (A220086/A220605)*(A220607/A220606) = A160389, which is the case n=7 of (Gamma(1/n)/Gamma(2/n))*(Gamma((n-1)/n)/Gamma((n-2)/n)) = 2*cos(Pi/n).

%C A220086*A220605*A220606*A220607*A220608*A220609 = (2*Pi)^3/sqrt(7), which is the case n=7 of product(Gamma(i/n), i=1..n-1) = sqrt((2*Pi)^(n-1)/n) (see also the second link to Wikipedia).

%C Continued fraction expansion: 6, 1, 1, 4, 1, 2, 2, 1, 5, 1, 10, 7, 1,...

%H Vincenzo Librandi, <a href="/A220086/b220086.txt">Table of n, a(n) for n = 1..1000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Particular_values_of_the_Gamma_function#General_rational_arguments">Particular values of the Gamma function: General rational arguments</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Particular_values_of_the_Gamma_function#Products">Particular values of the Gamma function: Products</a>

%H <a href="/index/Ga#gamma_function">Index to sequences related to the Gamma function</a>

%F Equals Pi*csc(Pi/7)/A220607, where csc is the cosecant function.

%e 6.5480629402478244377140933494289962626211351873841351...

%t RealDigits[Gamma[1/7], 10, 90][[1]]

%o (Maxima) fpprec:90; ev(bfloat(gamma(1/7)));

%o (PARI) default(realprecision, 100); gamma(1/7) \\ _G. C. Greubel_, Mar 10 2018

%o (MAGMA) SetDefaultRealField(RealField(100)); Gamma(1/7); // _G. C. Greubel_, Mar 10 2018

%K nonn,cons

%O 1,1

%A _Bruno Berselli_, Dec 12 2012

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Last modified April 18 06:48 EDT 2019. Contains 322209 sequences. (Running on oeis4.)