A360807 - OEIS

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A360807

Decimal expansion of Sum_{m>=1} 1/(1/4 + z(m)^2) where z(m) is the imaginary part of the m-th nontrivial zero of the Dirichlet beta function whose real part is 1/2.

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

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OFFSET

0,2

COMMENTS

Conjecture: Nontrivial zeros whose real part is not 1/2 do not exist.

LINKS

Table of n, a(n) for n=0..86.

Kano Kono, Summary Dirichlet beta function, Alien's Mathematics, p. 5.

FORMULA

Equals 4*log(Gamma(3/4)) + A001620/2 + log(2) - 3*log(Pi)/2.

Equals A074760 - 1 + log(4) - log(Pi) + 4*(log(Gamma(3/4)).

Equals 1 - A074760 + A001620 - 2*log(Pi) + 4*(log(Gamma(3/4)).