A note on some formulae related to Euler sums

Marc-Antoine Coppo (1) , Bernard Candelpergher (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

By employing the Ramanujan summation method, we derive some unusual formulas for a class of Euler sums (including divergent Euler sums) similar to the classical relations due to Euler.

Mots clés: Euler sums; analytic continuation; Ramanujan summation of series; harmonic numbers; series identities with special numbers; zeta values

Domaines: Théorie des nombres [math.NT]

Marc-Antoine Coppo, Bernard Candelpergher. A note on some formulae related to Euler sums. 2021. ⟨hal-03170892v2⟩