Some remarks on generalized Fibonacci and Lucas polynomials
Johann Cigler
TL;DR
This paper explores determinants of binomial coefficients related to generalized Fibonacci and Lucas polynomials, including their q-analogues, to extend understanding of their properties and relationships.
Contribution
It introduces new determinant formulas for generalized Fibonacci and Lucas polynomials and their q-analogues, expanding the theoretical framework of these sequences.
Findings
Derived determinant formulas for generalized Fibonacci polynomials
Extended results to q-analogues of these polynomials
Provided insights into the algebraic structure of these sequences
Abstract
Starting with some determinants of binomial coefficients which are related to Fibonacci and Lucas polynomials we study similar determinants for some generalizations of these polynomials and their q-analogues.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Mathematical Theories and Applications · Advanced Combinatorial Mathematics