Generalizations of the Bernoulli and Appell polynomials
Bretti, Gabriella ; Natalini, Pierpaolo ; Ricci, Paolo E.
Abstr. Appl. Anal., Tome 2004 (2004) no. 1, p. 613-623 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2004-06-29
Classification:  33C99,  34A35 
@article{1089229150,
     author = {Bretti, Gabriella and Natalini, Pierpaolo and Ricci, Paolo E.},
     title = {Generalizations of the Bernoulli and Appell polynomials},
     journal = {Abstr. Appl. Anal.},
     volume = {2004},
     number = {1},
     year = {2004},
     pages = { 613-623},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1089229150}
}

Bretti, Gabriella; Natalini, Pierpaolo; Ricci, Paolo E. Generalizations of the Bernoulli and Appell polynomials. Abstr. Appl. Anal., Tome 2004 (2004) no. 1, pp.  613-623. http://gdmltest.u-ga.fr/item/1089229150/