Monomiality and multi-index multi-variable special polynomials

In this paper, we will use the operational recipes from monomiality and umbral calculus to deal with multi-dimensional polynomials.

[1]  Giuseppe Dattoli,et al.  Evolution operator equations: Integration with algebraic and finitedifference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory , 1997 .

[2]  P. Appell,et al.  Fonctions hypergéométriques et hypersphériques : polynomes d'Hermite , 1926 .

[3]  J. L. Burchnall The Bessel Polynomials , 1951, Canadian Journal of Mathematics.

[4]  A. Turbiner,et al.  Lie-algebraic discretization of differential equations , 1995, funct-an/9501001.

[5]  Larry C. Andrews,et al.  Special functions for engineers and applied mathematicians , 1985 .

[6]  Giuseppe Dattoli,et al.  On Crofton–Glaisher type relations and derivation of generating functions for Hermite polynomials including the multi-index case , 2008 .

[7]  A. Wünsche Hermite and Laguerre 2D polynomials , 2001 .

[8]  D. Gershfeld,et al.  Special functions for engineers and applied mathematicians , 1986, IEEE Journal of Oceanic Engineering.

[9]  G. Dattoli Incomplete 2D Hermite polynomials: properties and applications , 2003 .

[10]  S. Lorenzutta,et al.  Theory of multiindex multivariable Bessel functions and Hermite polynomials , 1998 .

[11]  A. W. Kemp,et al.  A treatise on generating functions , 1984 .

[12]  Kraków,et al.  Representations of monomiality principle with Sheffer-type polynomials and boson normal ordering , 2005, quant-ph/0504009.

[13]  W. A. Al-Salam,et al.  The Bessel polynomials , 1957 .

[14]  Mourad E. H. Ismail,et al.  A -umbral calculus , 1981 .