On Nevai's bound for orthogonal polynomials associated with exponential weights (Q1084282)

Let \(\{p_ n\}\) be the sequence of orthonormal polynomials for the \(weight\quad function\) \(w(x)=\exp (-x^ m),\) for real x and \(m=2,4,6,..\). The author establishes some bounds on \(w(x)(p_ n(x)- p_{n-2}(x))^ 2\) and \(w(x)p^ 2_ n(x)\). He also studies the relation of the coefficient of the \(three-term\quad recurrence\) for \(\{p_ n\}\) to these bounds.