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<p>We introduce and investigate two new families of special polynomials: the mixed-type Fibonacci-Mittag-Leffler (FML) and Lucas-Mittag-Leffler (LML) polynomials. These are constructed by blending classical Fibonacci and Lucas polynomials with Mittag-Leffler polynomials, yielding novel recurrence relations and determinantal representations. Fundamental algebraic identities are established, and the zeros of these polynomials are analyzed through both analytic methods and computational visualization. The asymptotic behavior of zeros is further examined via a generalized version of Hurwitz theorem in two variables.</p>

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Mixed-type Fibonacci-Mittag-Leffler and Lucas-Mittag-Leffler polynomials: some properties

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月9日

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  • Can Kızılateş,
  • William Ramírez,
  • Yamilet Quintana,
  • Daniel Bedoya,
  • Maria-Fernanda Heredia-Moyano

摘要

We introduce and investigate two new families of special polynomials: the mixed-type Fibonacci-Mittag-Leffler (FML) and Lucas-Mittag-Leffler (LML) polynomials. These are constructed by blending classical Fibonacci and Lucas polynomials with Mittag-Leffler polynomials, yielding novel recurrence relations and determinantal representations. Fundamental algebraic identities are established, and the zeros of these polynomials are analyzed through both analytic methods and computational visualization. The asymptotic behavior of zeros is further examined via a generalized version of Hurwitz theorem in two variables.