Certain properties and numerical applications of generalized hybrid special polynomials associated with Hermite polynomials

Shahid Ahmad  Wani; Taghreed  Alqurashi; Juan Hernández; William  Ramírez; Jesús David Berrío  Valbuena

doi:10.5269/bspm.76485

Shahid Ahmad Wani
Taghreed Alqurashi
Juan Hernández Universidad Autónima de Santo Domingo
William Ramírez
Jesús David Berrío Valbuena

Abstract

This paper introduces a novel class of generalized Hermite-based Apostol-type Frobenius-Euler polynomials and numbers of order $\nu$ and level $\alpha$. We establish fundamental identities and properties by employing generating function techniques, including summation formulas, differential and integral relations, and addition theorems. Furthermore, we investigate their connections with Stirling numbers of the second kind and various other polynomial families. Additionally, we derive a corresponding differential equation and a recurrence relation for these newly defined polynomials. To visualize their behaviour, we utilize Maple to compute numerical values and illustrate the distribution of their zeros through surface plots.

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