Unconditional representations of the Euler-Mascheroni constant and the Bernoulli numbers via the Taylor coefficients of the Riemann ξ-function, and a hierarchy of exact relations at the central point

Nikos Mantzakouras, Carlos López

We give a self-contained, numerically verified derivation of three equivalent unconditional representations of the Euler--Mascheroni constant $\gamma$ as a rapidly convergent series in…