Zeros of Gegenbauer and Hermite polynomials and connection coefficients - Area, I; Dimitrov, D. K.; Godoy, E.; Ronveaux, A. (Amer Mathematical Soc, 2004)
In this paper, sharp upper limit for the zeros of the ultraspherical polynomials are obtained via a result of Obrechkoff and certain explicit connection coefficients for these polynomials. As a consequence, sharp bounds for the zeros of the Hermite polynomials are obtained.
Keywords: Orthogonal polynomials; zeros of Gegenbauer polynomials; zeros of Hermite polynomials; connection coefficients