On Turán’s inequality for ultraspherical polynomials
On Turán’s inequality for ultraspherical polynomials
(0.3) An,x(x) -[F,,x(x)]2 Fn+l,,(x)Fn_,iX(x) > or 1, where Fn,x(x) =P(x)(x)/P((1). V. R. Thiruvenkatachar and T. S. Nanjundiah [4] and A. E. Danese [5] have obtained series of positive functions for Ai\(x) and its analogue in the case of the ultraspherical, Laguerre and Hermite polynomials. In the present paper we deepen …