A New Effective Asymptotic Formula for the Stieltjes Constants

Lazhar Fekih-Ahmed (1)

1 ENIT - Ecole Nationale d'Ingénieurs de Tunis

We derive a new integral formula for the Stieltjes constants. The new formula permits easy computations as well as an exact approximate asymptotic formula. Both the sign oscillations and the leading order of growth are provided. The formula can also be easily extended to generalized Euler constants.

Mots clés: Stieltjes constants; Riemann Zeta function; Laurent expansion; asymptotic expansion

Domaines: Théorie des nombres [math.NT]

Lazhar Fekih-Ahmed. A New Effective Asymptotic Formula for the Stieltjes Constants. 2014. ⟨hal-01026562v3⟩