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

1,1

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.

Links

Table of n, a(n) for n=1..105.

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.

Formula

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

Example

2.942584772269271492842068894927865...

Mathematica

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

Crossrefs

Cf. A340711.

Sequence in context: A021038 A257818 A195485 * A011067 A135008 A200014

Adjacent sequences: A336799 A336800 A336801 * A336803 A336804 A336805

Keyword

nonn,cons

Author

Artur Jasinski, Jan 27 2021

Extensions

Name corrected by Alessandro Languasco, Feb 18 2021

Status

approved