Pascal Maroni, Manoubi Mejri

Generalized Bernoulli Polynomials Revisited and Some Other Appell Sequences

Abstract:
We study the problem posed by Nrlund in terms of dual sequences. We determine the functional equation fulfilled by the canonical form of any generalized Bernoulli sequence. Surprisingly these canonical forms are positive definite. Some results are given for an Euler sequence.

Keywords:
Orthogonal polynomials, dual sequences, Bernoulli and Euler polynomials.

MSC 2000: 42C05, 33C45