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A340884
Decimal expansion of the constant rho(1,5).
1
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
0,1
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.
LINKS
Steven Finch and Pascal Sebah, Residue of a Mod 5 Euler Product, arXiv:0912.3677 [math.NT], 2009 p. 1-2.
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).
EXAMPLE
0.249135702764931424659963795...
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Jan 25 2021
STATUS
approved