On the construction and structural analysis of Bell-enriched Appell-lambda polynomials via quasi-monomiality

Farukh Ahmed Mulani; Waseem Ahmad Khan; Shahid Ahmad Wani

doi:10.46481/jnsps.2026.3723

Authors

Farukh Ahmed Mulani
Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University) (SIU), Pune, India
Waseem Ahmad Khan
[email protected]

Department of Electrical Engineering, Prince Mohammad Bin Fahd University, P.O Box 1664, Al Khobar 31952, Saudi Arabia
Shahid Ahmad Wani
Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University) (SIU), Pune, India

Keywords:

λ-polynomials, Appell-λ-polynomials, Monomiality principle, Determinant approach, Graphical analysis

Abstract

A fresh class of hybrid special polynomials, termed the Bell-enriched Appell-lambda-polynomials, is constructed through the discrete convolution of Bell-based lambda-polynomials with the Appell sequence. A generating function for this class is established, from which closed-form expansions, convolution identities, and Stirling-number factorizations follow. The multiplicative and derivative operators that give this family its quasi-monomial character are identified, and the associated differential equation is recorded as an immediate corollary. A determinant representation `a la Wang is also obtained. To illustrate the scope of the general theory, three subfamilies are investigated: the Bell-enriched Bernoulli-lambda and Euler-lambda polynomials, which are admissible Appell specializations (mathcal{A}(0) neq 0), and the Bell-enriched Genocchi-lambda polynomials, which belong to the associated-Appell class (mathcal{A}(0)=0) and are treated separately. For the first two subfamilies, operational, quasi-monomial, and determinantal properties are fully established; for the Genocchi subfamily, generating-function and operational results are obtained within the associated-Appell framework. A numerical exploration of polynomial values, zero distributions, and graphical profiles supplements the algebraic development.

Dimensions

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