On Polynomials Satisfying a Turan Type Inequality

George Csordas, Jack Williamson
1974 Proceedings of the American Mathematical Society  
For Legendre polynomials Pn(x), P. Turan has established the inequality A"(X> = Pl(x) -P"+1(x)P"-l(x) ¡> 0, -liïSl.^1, with equality only for j-=±1. This inequality has generated considerable interest, and analogous inequalities have been extended to various classes of polynomials : ultraspherical, Laguerre, Hermite, and a class of Jacobi polynomials. Our purpose here is to determine necessary and sufficient conditions for a general class of polynomials to satisfy a Turan type inequality and to
more » ... characterize the generating functions of such a class.
doi:10.2307/2038898 fatcat:4ug2g5dnojgojlyctexlueh24i