Affiliation:
1. Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia
2. Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune, India
Abstract
<p>We present a novel framework for introducing generalized 3-variable 1-parameter Hermite-based Appell polynomials. These polynomials are characterized by generating function, series definition, and determinant definition, elucidating their fundamental properties. Moreover, utilizing a factorization method, we established recurrence relations, shift operators, and various differential equations, including differential, integrodifferential, and partial differential equations. Special attention is given to exploring the specific cases of 3-variable 1-parameter generalized Hermite-based Bernoulli, Euler, and Genocchi polynomials, offering insights into their unique features and applications.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference23 articles.
1. G. Dattoli, C. Chiccoli, S. Lorenzutta, G. Maino, A. Torre, Generalized Bessel functions and generalized Hermite polynomials, J. Math. Anal. Appl., 178 (1993), 509–516. https://doi.org/10.1006/jmaa.1993.1321
2. G. Dattoli, S. Lorenzutta, G. Maino, A. Torre, C. Cesarano, Generalized Hermite polynomials and super-Gaussian forms, J. Math. Anal. Appl., 203 (1996), 597–609. https://doi.org/10.1006/jmaa.1996.0399
3. P. Appell, J. K. de F${\acute{e}}$riet, Fonctions hyperg${\rm\acute{e}}$om${\rm\acute{e}}$triques et hypersph${\rm\acute{e}}$riques: polyn${\rm\hat{o}}$mes d' Hermite, Gauthier-Villars, Paris, 1926.
4. B. Yılmaz, M. A. Özarslan, Differential equations for the extended 2D Bernoulli and Euler polynomials, Adv. Differ. Equ., 2013 (2013), 107. https://doi.org/10.1186/1687-1847-2013-107
5. S. Khan, G. Yasmin, R. Khan, N. A. M. Hassan, Hermite-based Appell polynomials: properties and applications, J. Math. Anal. Appl., 351 (2009), 756–764. https://doi.org/10.1016/j.jmaa.2008.11.002