Convexity of the zeros of some orthogonal polynomials and related functions

We study convexity properties of the zeros of some special functions that follow from the convexity theorem of Sturm. We prove results on the intervals of convexity for the zeros of Laguerre, Jacobi and ultraspherical polynomials, as well as functions related to them, using transformations under whi...

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Veröffentlicht in:	Journal of computational and applied mathematics 2009-12, Vol.233 (3), p.762-767
Hauptverfasser:	Jordaan, Kerstin, Tookos, Ferenc
Format:	Artikel
Sprache:	eng
Schlagworte:	Convexity Exact sciences and technology Fourier analysis Jacobi polynomials Laguerre polynomials Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Orthogonal polynomials Sciences and techniques of general use Special functions Ultraspherical polynomials Zeros
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Beschreibung
Zusammenfassung:	We study convexity properties of the zeros of some special functions that follow from the convexity theorem of Sturm. We prove results on the intervals of convexity for the zeros of Laguerre, Jacobi and ultraspherical polynomials, as well as functions related to them, using transformations under which the zeros remain unchanged. We give upper as well as lower bounds for the distance between consecutive zeros in several cases.
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2009.02.045