Study on Morgan-Voyce type polynomials with Euler-Seidel algorithm
arXiv:2607.13489
The paper defines new families of Morgan‑Voyce type polynomials, derives their explicit formulas, recurrence relations and exponential generating functions, and links them to Euler‑Seidel matrices and binomial‑type sums for Bell polynomials.
Abstract
This paper bridges the domains of degenerate special polynomials, the Euler-Seidel matrix method, and Morgan-Voyce polynomials. We introduce two new families of Morgan-Voyce type polynomials and establish their structural properties, including explicit formulas and recurrence relations. Additionally, we define three polynomial variants and prove that three distinct binomial-type sums for Bell polynomials can be expressed as finite sums involving these new families, and derive their exponential generating functions. We then construct Euler-Seidel matrices using the initial sequences associated with Morgan-type polynomials. Our results yield novel algebraic identities and expand the application of matrix methods in combinatorial analysis.
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