**Pascal Maroni, Manoubi Mejri**

## Generalized Bernoulli
Polynomials Revisited and Some Other Appell Sequences

**Abstract:**

We study the problem posed by Nörlund 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