Some results involving Hermite-base polynomials and functions using operational methods

This paper is an attempt to stress the usefulness of the operational methods in the theory of special functions. Using operational methods, we derive summation formulae and generating relations involving various forms of Hermite-base polynomials and functions.

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

[2]  Willard Miller,et al.  Lie Theory and Special Functions , 1969 .

[3]  Subuhi Khan,et al.  Lie-theoretic generating relations of two variable Laguerre polynomials , 2003 .

[4]  Subuhi Khan,et al.  Operational methods: an extension from ordinary monomials to multi-dimensional Hermite polynomials , 2007 .

[5]  Elna Browning McBride Obtaining Generating Functions , 1971 .

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

[7]  G. Dattoli,et al.  Phase space formalism: The generalized harmonic-oscillator functions , 1995 .

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

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

[10]  Wilhelm Magnus,et al.  Lie Theory and Special Functions , 1969 .

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

[12]  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 .

[13]  Multivariable Lagrange Expansion and Generalization of Carlitz–Srivastava Mixed Generating Functions , 2001 .

[14]  Giuseppe Dattoli,et al.  Generalized polynomials and new families of generating functions , 2001, ANNALI DELL UNIVERSITA DI FERRARA.