Degenerate hybrid special polynomials associated with Fubini polynomials: properties and applications
Keywords:
Degenerate Hermite–Fubini polynomials, Monomiality principle, Operational identities, Zero distribution, Graphical representationAbstract
In this article, we introduce degenerate multivariate Hermite--based Fubini polynomials by convoluting three-variable degenerate Hermite and Fubini polynomials. First, we derive the generating function explicitly, specify the admissible parameter domain, and carry out a thorough study of its convergence behaviour, locating every singular point. Further, using operational formalism, we derive the quasi-monomial characteristics, including the differential equation satisfied by these polynomials. Algebraically, we derive a wide variety of formulae: series expansions, shifts in each variable separately, addition theorems, and recurrence relations. Many previously discovered polynomial families arise by specialization or limiting cases of the extra parameters, which provides further evidence of the generality of our approach. Along with the theoretical part, we carry out numerical computations of zeros for all degrees up to twenty-nine for several sets of parameters. Our results are presented graphically using zeros plotted on the complex plane, three-dimensional zero-trajectory plots, and tabulated numerical approximations; all of these point to conjugate symmetry properties of the roots and their systematic movement away from the origin.
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Copyright (c) 2027 Sarah Aljohani, Waseem Ahmad Khan, Fabio Fuentes-Gandara, Prakash Jadhav, Areefa Khatoon, Shahid Ahmad Wani (Author)
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