1bcaa76f-5306-4a8f-ba11-9a6c418fdfcc20220312062121722naun:naunmdt@crossref.orgMDT DepositInternational Journal of Mathematical Models and Methods in Applied Sciences1998-014010.46300/9101http://www.naun.org/cms.action?id=2820110202211020221610.46300/9101.2022.16https://npublications.com/journals/ijmmas/2022.phpC.CesaranoFaculty of Engineering, International Telematic University UNINETTUNO, Rome, ItalyDarioAssanteFaculty of Engineering, International Telematic University UNINETTUNO, Rome, ItalyBy 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.31220223122022778214https://npublications.com/journals/ijmmas/2022/a282001-014(2022).pdf10.46300/9101.2022.16.14https://npublications.com/journals/ijmmas/2022/a282001-014(2022).pdfAppell, P., Kampé de Fériet, J., “Fonctions hypergéométriques et hypersphériques. Polinomes d’Hermite”, Gauthier-Villars, Paris, 1926. 10.1016/s0022-247x(03)00259-2Dattoli, G., “Incomplete 2-D Hermite polynomials: Propeties and applications”, Journal of Mathematical Analysis and Applications, 284 (2), pp 447-454, 2003. 10.1063/1.530853Dodonov, V.V., Man’ko, V.I.,“New relations for two-dimensional Hermite polynomials”, Journal of mathematical Physics, 35 (8), pp. 4277-4294, 1994. 10.1215/s0012-7094-62-02907-1Gould, H.W., Hopper, A.T., “Operational formulas connected with two generalizations of Hermite polynomials”, Duke Math. J., 29, pp. 51-62, 1962. Srivastava, H.M., Manocha, H.L., “A treatise on generating functions”, Wiley, New York, 1984. Watson, J.H., “A treatise on Bessel functions”, Cambridge University press, 1958. Dattoli, G., Torre, A. “Theory and applications of generalized Bessel functions”, Aracne, Rome, 1996. Cesarano, C., Assante, D., “A note on generalized Bessel functions”, Int. J. of Math. Models and Methods in Appl. Sci., 7 (6), pp 625-629, 2013. 10.1016/j.amc.2011.01.082Aktas, R., Sahin, R., Altin, A., “On a multivariable extension of the Humbert polynomials”, Applied Mathematics and Computation, 218 (3), pp. 662-666, 2011. Cesarano, C., “Monomiality Principle and related operational techniques for Orthogonal Polynomials and Special Functions”, Int. J. of Math. Models and Methods in Appl. Sci., to appear, 2013. 10.1080/10652460412331270634Dattoli, G., Lorenzutta, S., Ricci, P.E., Cesarano, C., “On a family of hybrid polynomials”, Integral Transforms and Special Functions, 15 (6), pp. 485-490, (2004). Dattoli, G., Lorenzutta, Cesarano, C., “Bernestein polynomials and operational methods”, Journal of Computational Analysis and Applications, 8 (4), pp. 369-377, 2006. 10.1016/s0096-3003(00)00082-5Dattoli, G., Srivastava, H.M., Cesarano, C., “The Laguerre and Legendre polynomials from an operational point of view”, Applied Mathematics and Computation, 124 (1), pp. 117-127 (2001). 10.1016/s0096-3003(02)00328-4Dattoli, G., Cesarano, C., “On a new family of Hermite polynomials associated to parabolic cylinder functions”, applied Mathematics and Computation, 141 (1), pp. 143-149, 2003.