A340884 Decimal expansion of the constant rho(1,5).

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, 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, 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

Offset: 0

Author

Artur Jasinski, Jan 25 2021

Keywords

• nonn
• cons

Comments

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

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.

Examples

			0.249135702764931424659963795...
		

Links

• Steven Finch and Pascal Sebah, Residue of a Mod 5 Euler Product, arXiv:0912.3677 [math.NT], 2009 p. 1-2.

Crossrefs

Cf. A340628, A340808, A340004.

Formula

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

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

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

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