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New families of three-variable polynomials coupled with well-known polynomials and numbers

Kizilateş C. | Çekim B. | Tuğlu N. | Kim T.

Article | 2019 | Symmetry11 ( 2 )

In this paper, firstly the definitions of the families of three-variable polynomials with the new generalized polynomials related to the generating functions of the famous polynomials and numbers in literature are given. Then, the explicit representation and partial differential equations for new polynomials are derived. The special cases of our polynomials are given in tables. In the last section, the interesting applications of these polynomials are found. © 2019 by the authors.

A closed formula for the Horadam polynomials in terms of a tridiagonal determinant

Qi F. | Kizilateş C. | Du W.-S.

Article | 2019 | Symmetry11 ( 6 )

In this paper, the authors present a closed formula for the Horadam polynomials in terms of a tridiagonal determinant and, as applications of the newly-established closed formula for the Horadam polynomials, derive closed formulas for the generalized Fibonacci polynomials, the Lucas polynomials, the Pell-Lucas polynomials, and the Chebyshev polynomials of the first kind in terms of tridiagonal determinants. © 2019 by the authors.

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