Degenerate Euler–Seidel Matrix Method and Their Applications

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.