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Networks and Heterogeneous Media

2026, Volume 21, Issue 2: 551-563. doi: 10.3934/nhm.2026025
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Degenerate Euler–Seidel method for degenerate Bernoulli, Euler, and Genocchi polynomials

  • 1.
    Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
  • 2.
    Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
  • 3.
    Graduate School of Education, Yeungnam University, Gyeongsan 38541, Republic of Korea
  • Published: 08 April 2026

  • 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, thus providing a new framework to study their properties.

    Citation: Taekyun Kim, Dae San Kim, Hyunseok Lee, Kyo-Shin Hwang. Degenerate Euler–Seidel method for degenerate Bernoulli, Euler, and Genocchi polynomials[J]. Networks and Heterogeneous Media, 2026, 21(2): 551-563. doi: 10.3934/nhm.2026025

    Related Papers:

  • 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, thus providing a new framework to study their properties.



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