A335576 Decimal expansion of Mertens constant C(5,2).

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

Author

Artur Jasinski, Jan 26 2021

Keywords

• nonn
• cons

Comments

First 100 digits from Alessandro Languasco and Alessandro Zaccagnini 2007 p. 4.

Examples

			0.546975845411263480238301287430814...
		

Links

• Alessandro Languasco and Alessandro Zaccagnini, Computation of the Mertens constants - more than 100 correct digits, (2007), 1-134.

Crossrefs

Cf. A001620, A336798, A340004, A340127, A340213, A340665, A340794, A340839, A340866.

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)