DOIAbstract
AbstractLet wλ(x)≔(1−x2)λ−1/2 and Pn(λ) be the ultraspherical polynomials with respect to wλ(x). Then we denote En+1(λ) the Stieltjes polynomials with respect to wλ(x) satisfying∫−11wλ(x)Pn(λ)(x)En+1(λ)(x)xmdx=0,0⩽m<n+1,≠0,m=n+1.In this paper, we give estimates for the first and second derivatives of the Stieltjes polynomials En+1(λ) and the product En+1(λ)Pn(λ) by obtaining the asymptotic differential relations. Moreover, using these differential relations we estimate the second derivatives of En+1(λ)(x) and En+1(λ)(x)Pn(λ)(x) at the zeros of En+1(λ)(x) and the product En+1(λ)(x)Pn(λ)(x), respectively
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