A336802 Decimal expansion of the constant Pi(5, 1) [1/(residue at 1) of the Dedekind zeta function for the cyclotomic field Q(zeta_5)].

2, 9, 4, 2, 5, 8, 4, 7, 7, 2, 2, 6, 9, 2, 7, 1, 4, 9, 2, 8, 4, 2, 0, 6, 8, 8, 9, 4, 9, 2, 7, 8, 6, 5, 1, 3, 1, 8, 5, 5, 6, 3, 5, 9, 6, 2, 6, 3, 5, 7, 6, 7, 0, 7, 4, 5, 4, 2, 7, 9, 3, 7, 7, 4, 4, 1, 3, 6, 5, 4, 7, 9, 4, 3, 1, 8, 1, 6, 6, 5, 1, 4, 3, 4, 1, 9, 1, 4, 3, 1, 7, 1, 1, 7, 3, 5, 8, 6, 3, 2, 3, 1, 9, 8, 8

Offset: 1

Author

Artur Jasinski, Jan 27 2021

Keywords

• nonn
• cons

Comments

For general definition of constants Pi(q,a) see Alessandro Languasco and Alessandro Zaccagnini 2010 p. 19 eq (4), for this particular case see p. 25.

Examples

			2.942584772269271492842068894927865...
		

Links

• Alessandro Languasco and Alessandro Zaccagnini, On the constant in the Mertens product for arithmetic progressions. I. Identities, Funct. Approx. Comment. Math. Volume 42, Number 1 (2010), 17-27.
• For more links see A340711.

Crossrefs

Cf. A340711.

Programs

Mathematica

RealDigits[25 Sqrt[5]/(4 Pi^2 Log[1/2 (1 + Sqrt[5])]), 10, 105] // First

Formula

Equals 25*sqrt(5)/(4*Pi^2*log((1+sqrt(5))/2)).

Extensions

Name corrected by Alessandro Languasco, Feb 18 2021