Generalizations of the Bernoulli and Appell polynomials
By Gabriella Bretti, Pierpaolo Natalini, Paolo Emilio Ricci. 2004
47 citations recorded by the source corpus.
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-Kampe de Feriet (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.
Subfields: Algebra and Number Theory, Applied Mathematics, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/81423c63437a84dfba333b057441cd43f49a32c4
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Citations in the corpus
- Hermite-based Appell polynomials: Properties and applications (2009, background): “An(x)= B[m−1] n (x), m 1: The new generalized Bernoulli polynomials [5].”
- General-Appell Polynomials within the Context of Monomiality Principle (2013, background): “n ( x ) t n n ! Th en ew ge ne ra liz ed Be rn ou lli po ly no m ia ls [6 ]”