Degenerate Euler- Seidel Method for degenerate Bernoulli, Euler, and Genocchi polynomials

TL;DR

This paper extends the classical Euler-Seidel method to degenerate Bernoulli, Euler, and Genocchi polynomials by introducing a parameter lambda, leading to new identities and a generalized framework for these special polynomials.

Contribution

It introduces a degenerate Euler-Seidel method with a parameter lambda, establishing new identities and extending the classical approach to degenerate special polynomials.

Findings

Derived new combinatorial identities for degenerate polynomials

Established lambda-generalized binomial identities

Extended the Euler-Seidel method to degenerate cases

Abstract

This paper introduces a degenerate version of the Euler-Seidel method by incorporating a parameter lambda into the classical recurrence relation. We define a degenerate Euler-Seidel matrix associated with an initial sequence and establish corresponding lambda-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, providing a new framework for studying their properties.