Abstract
Related to generalized arithmetic triangle, we introduce the hyper (r, q)-Fibonacci polynomials as the sum of these elements along a finite ray starting from a specific point, which generalize the hyper-Fibonacci polynomials. We give generating function, recurrence relations and we show some properties whose application allows us to extend the notion of Cassini determinant and to study some ratios. Moreover, we derive a connection between these polynomials and the incomplete (r, q)-Fibonacci polynomials defined in this paper.
This work is partially supported by DGRSDT Grant no 0656701.
(Communicated by István Gaál)
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© 2024 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Prof. RNDr. Gejza Wimmer, DrSc. – 3/4 C?
- On hyper (r, q)-Fibonacci polynomials
- The pointfree version of 𝓒c(X) via the ranges of functions
- On the x-coordinates of Pell equations that are products of two Pell numbers
- Subordination properties and coefficient problems for a novel class of convex functions
- Certain radii problems for 𝓢∗(ψ) and special functions
- On direct and inverse Poletsky inequalities with a tangential dilatation
- Fourth-order nonlinear strongly non-canonical delay differential equations: new oscillation criteria via canonical transform
- Hermite interpolation of type total degree associated with certain spaces of polynomials
- Decomposition in direct sum of seminormed vector spaces and Mazur–Ulam theorem
- A fixed point technique to the stability of Hadamard 𝔇-hom-der in Banach algebras
- Compact subsets of Cλ,u(X)
- Variations of star selection principles on hyperspaces
- On lower density operators
- Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠2t,3
- On the von Bahr–Esseen inequality for pairwise independent random vectors in Hilbert spaces with applications to mean convergence
- Large deviations for some dependent heavy tailed random sequences
- Metric, stratifiable and uniform spaces of G-permutation degree
- In memory of Paolo
Articles in the same Issue
- Prof. RNDr. Gejza Wimmer, DrSc. – 3/4 C?
- On hyper (r, q)-Fibonacci polynomials
- The pointfree version of 𝓒c(X) via the ranges of functions
- On the x-coordinates of Pell equations that are products of two Pell numbers
- Subordination properties and coefficient problems for a novel class of convex functions
- Certain radii problems for 𝓢∗(ψ) and special functions
- On direct and inverse Poletsky inequalities with a tangential dilatation
- Fourth-order nonlinear strongly non-canonical delay differential equations: new oscillation criteria via canonical transform
- Hermite interpolation of type total degree associated with certain spaces of polynomials
- Decomposition in direct sum of seminormed vector spaces and Mazur–Ulam theorem
- A fixed point technique to the stability of Hadamard 𝔇-hom-der in Banach algebras
- Compact subsets of Cλ,u(X)
- Variations of star selection principles on hyperspaces
- On lower density operators
- Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠2t,3
- On the von Bahr–Esseen inequality for pairwise independent random vectors in Hilbert spaces with applications to mean convergence
- Large deviations for some dependent heavy tailed random sequences
- Metric, stratifiable and uniform spaces of G-permutation degree
- In memory of Paolo