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arXiv · 2512.20078

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

Taekyun Kim·Dae San Kim·Hyunseok Lee·Kyo-Shin Hwang
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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.

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Taekyun Kim, Dae San Kim, Hyunseok Lee, Kyo-Shin Hwang. 2025-12-23. Degenerate Euler- Seidel Method for degenerate Bernoulli, Euler, and Genocchi polynomials. https://arxiv.org/abs/2512.20078

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