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Abstract: The family of general Jacobi polynomials where can be characterised by complex (non-Hermitian) orthogonality relations (cf. Kuijlaars et al. (2005)). The special subclass of Jacobi polynomials where are classical and the real orthogonality, quasi-orthogonality as well as related properties, such as the behaviour of the real zeros, have been well studied. There is another special subclass of Jacobi polynomials with , which are known as Pseudo-Jacobi polynomials. The sequence of Pseudo-Jacobi polynomials is the only other subclass in the general Jacobi family (beside the classical Jacobi polynomials) that has real zeros for every for certain values of . For some parameter ranges Pseudo-Jacobi polynomials are fully orthogonal, for others there is only complex (non-Hermitian) orthogonality. We summarise the orthogonality and quasi-orthogonality properties and study the zeros of Pseudo-Jacobi polynomials, providing asymptotics, bounds and results on the monotonicity and convexity of the zeros. [Copyright &y& Elsevier]

Abstract: We use mixed three term recurrence relations typically satisfied by classical orthogonal polynomials from sequences corresponding to different parameters to derive upper (lower) bounds for the smallest (largest) zeros of Jacobi, Laguerre and Gegenbauer polynomials. [Copyright &y& Elsevier]

Abstract: We prove that the zeros of some families of hypergeometric polynomials are all real and negative. This result has a connection with the theory of Pólya frequency sequences and functions. As a consequence, we establish the asymptotic distribution of these zeros when the degree of the polynomials tends to infinity. [Copyright &y& Elsevier]