Let and be the ultraspherical polynomials with respect to . Then, we denote the Stieltjes polynomials with respect to by satisfying , , , . In this paper, we investigate asymptotic properties of derivatives of the Stieltjes polynomials and the product . Especially, we estimate the even-order derivative values of and at the zeros of and the product , respectively. Moreover, we estimate asymptotic representations for the odd derivatives values of and at the zeros of and on a closed subset of , respectively. These estimates will play important roles in investigating convergence and divergence of the higher-order Hermite-Fejér interpolation polynomials.
Hee Sun Jung. Ryozi Sakai. "Asymptotic Properties of Derivatives of the Stieltjes Polynomials." J. Appl. Math. 2012 1 - 25, 2012. https://doi.org/10.1155/2012/482935