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Articles

Discrete semi-classical orthogonal polynomials of class one on quadratic lattices

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Pages 1-20 | Received 13 Jan 2018, Accepted 07 Nov 2018, Published online: 04 Dec 2018
 

ABSTRACT

We study orthogonal polynomials on quadratic lattices with respect to Stieltjes functions, S, that satisfy a difference equation ADS=CMS+D, where A is a polynomial of degree less or equal than 3 and C is a polynomial of degree greater or equal than 1 and less or equal than 2. We show systems of difference equations for the orthogonal polynomials that arise from the so-called compatibility conditions. Some closed formulae for the recurrence relation coefficients are obtained.

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

Acknowledgements

The authors are grateful to the anonymous referee for useful comments, and for pointing out reference [Citation16].

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

GF acknowledges the support of the National Science Center (Poland) via grant no. OPUS 2017/25/B/BST1/00931. Support of the Alexander von Humboldt Foundation is also greatfully acknowledged. The work of MNR was partially supported by the Centre for Mathematics of the University of Coimbra – UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.

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