Year: 2026
Type: article
Abstract: In this study, we systematically construct a novel framework within umbral calculus by integrating the structures of generalized F ‐calculus and degenerate sequences. Utilizing Roman’s foundational approach to umbral calculus, we first introduce a new family of ψ − F − linear functionals and their corresponding ψ − F − differential operators on the polynomial space. Based on these operational tools, we define a generalized class of polynomials designated as the ψ − Sheffer F − polynomials s u , F , ψ ( x ) and explicitly demonstrate their degenerate sequences. Furthermore, we extend this construction to matrix theory by defining the degenerate Fibo–Bernoulli matrix , the generalized degenerate Fibo–Pascal matrix , and the degenerate Fibo–Euler matrix . Finally, we establish the algebraic relationships and structural connections among these newly introduced degenerate matrices. The results obtained herein provide an organized algebraic bridge between degenerate Sheffer sequences and Fibonacci‐based matrix representations.
Source: Journal of Mathematics
DOI: 10.1155/jom/9940913
Author: Semra Kuş
Institution: Ahi Evran University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,160
OpenAlex ID: W7212182003