Degenerate Euler–Seidel method for degenerate Bernoulli, Euler, and Genocchi polynomials

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Abstract

This paper introduces a degenerate version of the Euler–Seidel method by incorporating a parameter λ into the classical recurrence relation. We define a degenerate Euler–Seidel matrix associated with an initial sequence and establish corresponding λ-generalized binomial identities and generating function relations. By applying this method to the degenerate Bernoulli, Euler, and Genocchi polynomials, we derive several new combinatorial identities. This work extends the classical Euler– Seidel method to the domain of degenerate special polynomials and numbers, thus providing a new framework to study their properties.

Keywords

degenerate Euler–Seidel matrix / degenerate Bernoulli polynomial / degenerate Euler polynomial / degenerate Genocchi polynomial

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