Degenerate Euler–Seidel Matrix Method and Their Applications

Mathematical Methods in the Applied Sciences 2026

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Authors: Taekyun Kim, Dae San Kim
DOI: 10.1002/mma.70468
Cited by: 2
References: 13

Abstract

ABSTRACT This paper introduces a degenerate version of the Euler–Seidel matrix method by incorporating a parameter into the classical recurrence relation. The standard Euler–Seidel method relates the generating functions of an initial sequence and its final sequence via Seidel's formula, . Our generalized method establishes transformation formulas using ‐generalized binomial identities and yields a degenerate Seidel's formula for the exponential generating functions: . The results are applied to study and derive new combinatorial identities for sequences like the degenerate Bell and Fubini numbers and polynomials.

Fields of Study & Subjects

Advanced Mathematical Theories and Applications Advanced Combinatorial Mathematics Advanced Mathematical Identities

Publication details

Journal / source
Mathematical Methods in the Applied Sciences
Publisher
Wiley
Volume
49
Issue
8
Pages
8209–8223
Publication date
7 January 2026
Language
EN