Quasi-orthogonality of some hypergeometric polynomials

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dc.contributor.author Johnston, S.J.
dc.contributor.author Jordaan, Kerstin Heidrun
dc.contributor.author Jooste, Alta
dc.date.accessioned 2015-11-16T10:05:51Z
dc.date.issued 2016
dc.description.abstract The zeros of quasi-orthogonal polynomials play a key role in applications in areas such as interpolation theory, Gauss-type quadrature formulas, rational approximation and electrostatics. We extend previous results on the quasi-orthogonality of Jacobi polynomials and discuss the quasi-orthogonality of Meixner–Pollaczek, Hahn, Dual- Hahn and Continuous Dual-Hahn polynomials using a characterization of quasi-orthogonality due to Shohat. Of particular interest are the Meixner–Pollaczek polynomials whose linear combinations only exhibit quasi-orthogonality of even order. In some cases, we also investigate the location of the zeros of these polynomials for quasiorthogonality of order 1 and 2 with respect to the end points of the interval of orthogonality, as well as with respect to the zeros of different polynomials in the same orthogonal sequence. en_ZA
dc.description.embargo 2017-04-30
dc.description.librarian hb2015 en_ZA
dc.description.sponsorship National Research Foundation of South Africa [grant number 2054423]. en_ZA
dc.description.uri http://www.tandfonline.com/loi/gitr20 en_ZA
dc.identifier.citation S.J. Johnston, A. Jooste & K. Jordaan (2016) Quasi-orthogonality of some hypergeometric polynomials, Integral Transforms and Special Functions, 27:2, 111-125, DOI: 10.1080/10652469.2015.1098635. en_ZA
dc.identifier.issn 1065-2469 (print)
dc.identifier.issn 1476-8291 (online)
dc.identifier.other 10.1080/10652469.2015.1098635
dc.identifier.uri http://hdl.handle.net/2263/50490
dc.language.iso en en_ZA
dc.publisher Taylor and Francis en_ZA
dc.rights © 2015 Taylor and Francis. This is an electronic version of an article published in Integral Transforms and Special Functions, vol. 27, no. 2, pp. 111-125, 2016. doi : 10.1080/10652469.2015.1098635. Integral Transforms and Special Functions is available online at : http://www.tandfonline.comloi/gitr20. en_ZA
dc.subject Hypergeometric polynomials en_ZA
dc.subject Quasi-orthogonal polynomials en_ZA
dc.subject Zeros en_ZA
dc.subject pFq polynomials en_ZA
dc.title Quasi-orthogonality of some hypergeometric polynomials en_ZA
dc.type Postprint Article en_ZA


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