Convexity of the zeros of some orthogonal polynomials and related functions

✍ Scribed by Kerstin Jordaan; Ferenc Tookos

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 366 KB
• Volume: 233
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.02.045

✦ Synopsis

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.