This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A220086 #70 May 22 2025 01:08:29 %S A220086 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 A220086 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 A220086 7,6,2,0,4,7,3,8,2,3,9,1,3,7,7,9,0,5,6 %N A220086 Decimal expansion of Gamma(1/7). %C A220086 (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 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 A220086 Continued fraction expansion: 6, 1, 1, 4, 1, 2, 2, 1, 5, 1, 10, 7, 1,... %H A220086 Vincenzo Librandi, <a href="/A220086/b220086.txt">Table of n, a(n) for n = 1..1000</a> %H A220086 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 A220086 Wikipedia, <a href="http://en.wikipedia.org/wiki/Particular_values_of_the_Gamma_function#Products">Particular values of the Gamma function: Products</a> %H A220086 <a href="/index/Ga#gamma_function">Index to sequences related to the Gamma function</a> %F A220086 Equals Pi * csc(Pi/7) / A220607, where csc is the cosecant function. %F A220086 (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). %F A220086 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). %F A220086 A220086*A220607 = A220605*A220606 + A220608*A220609. - _Andrea Pinos_, May 21 2025 %e A220086 6.5480629402478244377140933494289962626211351873841351... %t A220086 RealDigits[Gamma[1/7], 10, 90][[1]] %o A220086 (Maxima) fpprec:90; ev(bfloat(gamma(1/7))); %o A220086 (PARI) default(realprecision, 100); gamma(1/7) \\ _G. C. Greubel_, Mar 10 2018 %o A220086 (Magma) SetDefaultRealField(RealField(100)); Gamma(1/7); // _G. C. Greubel_, Mar 10 2018 %K A220086 nonn,cons %O A220086 1,1 %A A220086 _Bruno Berselli_, Dec 12 2012