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A335576
Decimal expansion of Mertens constant C(5,2).
1
5, 4, 6, 9, 7, 5, 8, 4, 5, 4, 1, 1, 2, 6, 3, 4, 8, 0, 2, 3, 8, 3, 0, 1, 2, 8, 7, 4, 3, 0, 8, 1, 4, 0, 3, 7, 7, 5, 1, 9, 9, 6, 3, 2, 4, 1, 0, 0, 8, 1, 9, 2, 9, 5, 1, 5, 3, 1, 2, 7, 1, 8, 7, 1, 9, 1, 7, 5, 1, 8, 1, 1, 0, 8, 5, 7, 1, 5, 1, 6, 6, 8, 3, 3, 5, 8, 4, 0, 6, 3, 7, 2, 3, 8, 3, 5, 4, 8, 2, 3
OFFSET
0,1
COMMENTS
First 100 digits from Alessandro Languasco and Alessandro Zaccagnini 2007 p. 4.
LINKS
Alessandro Languasco and Alessandro Zaccagnini, Computation of the Mertens constants - more than 100 correct digits, (2007), 1-134.
FORMULA
A = C(5,1)=1.2252384385390845800576097747492205... see A340839.
B = C(5,2)=0.5469758454112634802383012874308140... this constant.
C = C(5,3)=0.8059510404482678640573768602784309... see A336798.
D = C(5,4)=1.2993645479149779881608400149642659... see A340866.
A*B*C*D = 0.70182435445860646228... = (5/4)*exp(-gamma), where gamma is the Euler-Mascheroni constant A001620.
B = sqrt(2)*5^(3/4)*sqrt(A340127)*exp(-gamma)/(4*sqrt(A340004)*A^2*C).
B = 2*A*D*log((1+sqrt(5))/2)/(C*sqrt(5)*A340794*A340665).
B = A*D*log((1+sqrt(5))/2)^2/(C*Pi*A340213^2).
From Vaclav Kotesovec, Jan 27 2021: (Start)
B*C = 5^(1/4) * exp(-gamma/2) * sqrt(log((1+sqrt(5))/2) / (2 * A340665 * A340794)).
A*D = 5^(3/4) * exp(-gamma/2) * sqrt(A340665 * A340794 / (8 * log((1+sqrt(5))/2))).
(End)
EXAMPLE
0.546975845411263480238301287430814...
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Jan 26 2021
STATUS
approved