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Jordaan, K.* ; Toókos, F.

Orthogonality and asymptotics of pseudo-Jacobi polynomials for non-classical parameters.

J. Approx. Theory 178, 1-12 (2014)
DOI
Open Access Green as soon as Postprint is submitted to ZB.
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 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 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 n real zeros for every n=0,1,2,… for certain values of α∈C. 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.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Orthogonal polynomials; Quasi-orthogonal polynomials; Jacobi polynomials with complex parameters; Pseudo-Jacobi polynomials; Zeros; Valued Weight Function; Extreme Zeros
ISSN (print) / ISBN 0021-9045
e-ISSN 1096-0430
Journal Journal of Approximation Theory
Quellenangaben Volume: 178, Issue: , Pages: 1-12 Article Number: , Supplement: ,
Publisher Elsevier
Reviewing status Peer reviewed
Institute(s) Institute of Computational Biology (ICB)