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Mixed-type Fibonacci-Mittag-Leffler and Lucas-Mittag-Leffler polynomials: some properties
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Abstract
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.
Springer Science and Business Media LLC
Title: Mixed-type Fibonacci-Mittag-Leffler and Lucas-Mittag-Leffler polynomials: some properties
Description:
Abstract
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.
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