Abstract
In this paper, based on the (p, q)-Fibonacci polynomials and (p, q)-Lucas polynomials
, we introduce the convolved (p, q)-Fibonacci polynomials
, which generalize the convolved Fibonacci numbers, the convolved Pell polynomials, and the Gegenbauer polynomials. We give the expressions, expansions, recurrence relations and differential recurrence relations of
, and establish the relations between
,
and
. Moreover, we also study the determinantal representations of
and
, and present an algebraic interpretation of the polynomials
.
Acknowledgments
The authors would like to thank the anonymous referee for his (her) valuable comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.