A371881 - OEIS

%I #35 Apr 21 2024 07:35:37

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

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

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

%N Decimal expansion of Gamma(1/20).

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

%F Equals 2^(33/40) * 5^(5/16) * (1 + sqrt(5))^(1/8) * sqrt(5^(1/4) + sqrt(2 + sqrt(5))) * sqrt(Pi*Gamma(1/10)) * QPochhammer(exp(-2*sqrt(5)*Pi)) / exp(sqrt(5)*Pi/12).

%e 19.4700853112555128640473209677271275456304195833419756810827837553645...

%p evalf(GAMMA(1/20), 130);  # _Alois P. Heinz_, Apr 15 2024

%t RealDigits[Gamma[1/20], 10, 120][[1]]

%t RealDigits[2^(33/40) * 5^(5/16) * (1 + Sqrt[5])^(1/8) * Sqrt[5^(1/4) + Sqrt[2 + Sqrt[5]]] * Sqrt[Pi * Gamma[1/10]] * QPochhammer[E^(-2*Sqrt[5]*Pi)] / E^(Sqrt[5]*Pi/12), 10, 120][[1]]

%Y Cf. A073005, A175380, A256191, A203140, A371983.

%K nonn,cons

%O 2,2

%A _Vaclav Kotesovec_, Apr 15 2024