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A340866 Decimal expansion of the Mertens constant C(5,4).

%I A340866 #33 Sep 27 2024 07:58:02
%S A340866 1,2,9,9,3,6,4,5,4,7,9,1,4,9,7,7,9,8,8,1,6,0,8,4,0,0,1,4,9,6,4,2,6,5,
%T A340866 9,0,9,5,0,2,5,7,4,9,7,0,4,0,8,3,2,9,6,6,2,0,1,6,7,8,1,7,7,0,3,1,2,9,
%U A340866 2,2,8,7,8,8,3,5,4,4,0,3,5,8,0,6,4,7,6,4,7,6,9,7,6,7,6,5,7,9,3,0,2,9,4,0,9,3,5,5,0,7,6,3,7,3,7,4,3,2,1,5,4,2,7,1,1,9,0,7,0,3,3,5,4,0,9,8,6,0,6,1,4,5,0,3,2,9,7,2,5,8,8,4,3,6,1,1,5,9,8
%N A340866 Decimal expansion of the Mertens constant C(5,4).
%C A340866 Data taken from Alessandro Languasco and Alessandro Zaccagnini 2007 p. 4.
%D A340866 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.2 Meissel-Mertens constants (pp. 94-95).
%H A340866 Vaclav Kotesovec, <a href="/A340866/b340866.txt">Table of n, a(n) for n = 1..497</a>
%H A340866 Alessandro Languasco and Alessandro Zaccagnini, <a href="https://doi.org/10.1090/S0025-5718-08-02148-0">On the constant in the Mertens product for arithmetic progressions. II: Numerical values</a>, Math. Comp. 78 (2009), 315-326.
%H A340866 Alessandro Languasco and Alessandro Zaccagnini, <a href="https://www.dei.unipd.it/~languasco/MCcomput/MCfinalresults.pdf"> Computation of the Mertens constants - more than 100 correct digits</a>, (2007). [in this table on page 4, the last correct digit is a(108), beyond the level there certified. - _Vaclav Kotesovec_, Jan 26 2021]
%H A340866 Alessandro Languasco and Alessandro Zaccagnini, <a href="https://projecteuclid.org/euclid.facm/1269437065">On the constant in the Mertens product for arithmetic progressions. I. Identities</a>, Funct. Approx. Comment. Math. Volume 42, Number 1 (2010), 17-27.
%H A340866 For other links see A340711.
%F A340866 Equals A340839*5^(1/4)*sqrt(A340004/(2*A340127)).
%F A340866 Equals (13*Pi^2/(24*sqrt(5)*exp(gamma)*log((1+sqrt(5))/2))*A340629/A340809)^(1/4). - _Vaclav Kotesovec_, Jan 25 2021
%e A340866 1.299364547914977988160840014964265909502574970408329662016...
%t A340866 (* Using Vaclav Kotesovec's function Z from A301430. *)
%t A340866 $MaxExtraPrecision = 1000; digits = 121;
%t A340866 digitize[c_] := RealDigits[Chop[N[c, digits]], 10, digits - 1][[1]];
%t A340866 digitize[(13*Pi^2 / (24*Sqrt[5] * Exp[EulerGamma] * Log[(1 + Sqrt[5])/2]) * Z[5, 1, 2]^2 / (Z[5, 1, 4] * Z[5, 4, 4]))^(1/4)]
%Y A340866 Cf. A340004, A340127, A340839, A340711.
%K A340866 nonn,cons
%O A340866 1,2
%A A340866 _Artur Jasinski_, Jan 24 2021
%E A340866 Corrected by _Vaclav Kotesovec_, Jan 25 2021
%E A340866 More digits from _Vaclav Kotesovec_, Jan 26 2021