In this paper, we give some determinantal and permanental representations of generalized bivariate Lucas p-polynomials by using various Hessenberg matrices. The results that we obtained are important since generalized bivariate Lucas p-polynomials are general forms of, for example, bivariate Jacobsthal-Lucas, bivariate Pell-Lucas ppolynomials, Chebyshev polynomials of the first kind, Jacobsthal...

The family of general Jacobi polynomials P (α,β) n where α, β ∈ C can be characterised by complex (nonhermitian) orthogonality relations (cf. [15]). The special subclass of Jacobi polynomials P (α,β) n where α, β ∈ R are classical and the real orthogonality, quasi-orthogonality as well as related properties, such as the behaviour of the n real zeros, have been well studied. There is another spe...