Multidimensional extensions of the Bernoulli and Appell polynomials (Q1769527)

The present paper deals with the so-called multidimensional extensions of the Bernoulli and Appell polynomials obtained generalizing the corresponding generating functions, and using the Hermite-Kampé de Fériet (or Gould-Hopper) polynomials. Here, by using the classical factorization method for differential equation (usually called the Infeld and Hull method after the paper [\textit{L. Infeld} and \textit{T. E. Hull}, ``The factorization method'', Rev. Mod. Phys. 23, 21--68 (1951; Zbl 0043.38602)], the author derives the corresponding differential equations satisfied by the two-dimensional polynomials. Finally, some other properties such as the three-term recurrence relation is obtained.