Convexity of the largest zero of the ultraspherical polynomials

Abstract

Let , be the kth positive zero in decreasing order of the Ultraspherical polynomials . It is proved that the largest positive zero of the polynomials is a convex function of λ for .

Keywords:

• zeros of ultraspherical polynomials
• convexity of the largest zero

MSC(1991):

• 33A45
• 33A65