On Two Applications of Herschel's Theorem

Lazhar Fekih-Ahmed (1)

1 ENIT - Ecole Nationale d'Ingénieurs de Tunis

As a first application of a very old theorem, known as Herschel's theorem, we provide direct elementary proofs of several explicit expressions for some numbers and polynomials that are known in combinatorics. The second application deals with the analytical continuation of the polylogarithmic function of complex argument beyond the circle of convergence.

Mots clés: Herschel's theorem; Bernoulli Numbers; Euler Numbers; Eulerian Numbers; Genocchi numbers; Polylogarithms

Domaines: Théorie des nombres [math.NT]

Lazhar Fekih-Ahmed. On Two Applications of Herschel's Theorem. 2012. ⟨hal-00693295⟩