Generalized Bernoulli numbers and a formula of Lucas

Victor H. Moll (1) , Christophe Vignat (2)

1 Department of Mathematics [Tulane, New Orleans]
2 L2S - Laboratoire des signaux et systèmes

An overlooked formula of E. Lucas for the generalized Bernoulli numbers is proved using generating functions. This is then used to provide a new proof and a new form of a sum involving classical Bernoulli numbers studied by K. Dilcher. The value of this sum is then given in terms of the Meixner-Pollaczek polynomials.

Domaines: Probabilités [math.PR]

Victor H. Moll, Christophe Vignat. Generalized Bernoulli numbers and a formula of Lucas. The Fibonacci Quarterly, 2015, 53 (4), pp.349. ⟨hal-01322848⟩