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In the present study, by the motivation of the papers in the literature, we initially characterize k-order Jacobsthal polynomials and establish the general form for the powers of their related class of companion matrices. More precisely, we give some explicit formulas of the entries of the powers \(Q^n_k(x)\) via the Fibonacci-Jacobsthal fundamental system. Consequently, this approach allows us to shed light on studies on Jacobsthal polynomials.

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On k-Order Jacobsthal Polynomials and Their Properties

  • 会议论文

  • 发表日期：

    2025年

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  • Samet Arpacı,
  • Fatih Yılmaz

摘要

In the present study, by the motivation of the papers in the literature, we initially characterize k-order Jacobsthal polynomials and establish the general form for the powers of their related class of companion matrices. More precisely, we give some explicit formulas of the entries of the powers \(Q^n_k(x)\) via the Fibonacci-Jacobsthal fundamental system. Consequently, this approach allows us to shed light on studies on Jacobsthal polynomials.