WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
Humbert Polynomials and Functions in Terms of Hermite Polynomials Towards Applications to Wave Propagation
Authors: Clemente Cesarano, Gerardo Maria Cennamo, Luca Placidi
Abstract: By starting from the standard definitions of the incomplete two-variable Hermite polynomials, we propose non-trivial generalizations and we show some applications to the Bessel-type functions as the Humbert functions. We also present a generalization of the Laguerre polynomials in the same context of the incomplete-type and we use these to obtain relevant operational techniques for the Humbert-type functions. Final considerations are inserted to include the problem of wave propagation in the present theoretical framework.
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Keywords: Hermite Polynomials, Laguerre polynomials, Generating Functions, Orthogonal Polynomials, Humbert polynomials, Humbert Functions, Bessel Functions
Pages: 595-602
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #58