A340884 - OEIS

%I #24 Jan 26 2021 11:57:21

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

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

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

%N Decimal expansion of the constant rho(1,5).

%C From definition Steven Finch and Pascal Sebah 2009 p. 1:

%C rho(n,m) = lim_{s->1} (s-1) Product_{primes p==n (mod m)} (1-1/p^s)^phi(m), where phi(n) = A000010(n) is the Euler totient function.

%H Steven Finch and Pascal Sebah, <a href="https://arxiv.org/abs/0912.3677">Residue of a Mod 5 Euler Product</a>, arXiv:0912.3677 [math.NT], 2009 p. 1-2.

%F Equals 1/(exp(gamma)*A340839^4).

%F Formulas by Steven Finch and Pascal Sebah 2009 p. 2.

%F Equals 5*log(2 + sqrt(5))*A340004^2/(3*Pi^2).

%F Equals 50*log(2 + sqrt(5))*A340808/(13*Pi^2*sqrt(5)*A340628).

%e 0.249135702764931424659963795...

%Y Cf. A340628, A340808, A340004.

%K nonn,cons

%O 0,1

%A _Artur Jasinski_, Jan 25 2021