The Generalized Binomial Transform of the Bivariate Fibonacci and Lucas $p$-Polynomials

The generalized binomial transforms of the bivariate Fibonacci $p-$polynomials and Lucas $p-$polynomials are introduced in this study. Furthermore, the generating functions of these polynomials are provided. Moreover, some relations are found for them. All results obtained are reduced to the $k-$binomial, falling binomial, rising binomial, and binomial transforms of the Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Fibonacci, and Lucas numbers.

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Publication Details

Journal
Mathematical Sciences and Applications E-Notes
Published
2025-05-19
DOI
https://doi.org/10.36753/mathenot.1607457
Primary Topic
Advanced Mathematical Theories and Applications
Type
article
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article

The Generalized Binomial Transform of the Bivariate Fibonacci and Lucas $p$-Polynomials

Yasemin Alp
Mathematical Sciences and Applications E-Notes
Advanced Mathematical Theories and Applications
article

The Generalized Binomial Transform of the Bivariate Fibonacci and Lucas $p$-Polynomials

Yasemin Alp
article en

Abstract

The generalized binomial transforms of the bivariate Fibonacci $p-$polynomials and Lucas $p-$polynomials are introduced in this study. Furthermore, the generating functions of these polynomials are provided. Moreover, some relations are found for them. All results obtained are reduced to the $k-$binomial, falling binomial, rising binomial, and binomial transforms of the Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Fibonacci, and Lucas numbers.

Mathematical Sciences and Applications E-NotesVol. 13(2)
Selçuk University (TR)
Openalex Percentile: Top 91%
Advanced Mathematical Theories and Applications
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