Georgian Mathematical Journal 12 (2005), No. 4, 697--716
Copyright Heldermann Verlag 2005
Generalized Bernoulli Polynomials Revisited and Some Other Appell Sequences
Pascal Maroni
Lab. Jacques-Louis Lions, Université Pierre Marie Curie, Boite Courrier 187, 75252 Paris Cedex 05, France
maroni@ann.jussieu.fr
Manoubi Mejri
Institut Supérieure des Sciences Appl. Tech., Rue Omar Ibn El Khattab, Gabčs 6072, Tunisia
manoubi.mejri@issatgb.rnu.tn
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: 42C05, 33C45
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