Gabriella Bretti, Pierpaolo Natalini, Paolo E. Ricci, "Generalizations of the Bernoulli and Appell polynomials", Abstract and Applied Analysis, vol. 2004, Article ID 350120, 11 pages, 2004. https://doi.org/10.1155/S1085337504306263
Generalizations of the Bernoulli and Appell polynomials
We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions. Furthermore, multidimensional extensions of the Bernoulli and Appell polynomials are derived generalizing the relevant generating functions, and using the Hermite-Kampé de Fériet (or Gould-Hopper) polynomials. The main properties of these polynomial sets are shown. In particular, the differential equations can be constructed by means of the factorization method.
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