Exact bounds for orthogonal polynomials associated with exponential weights (Q1084281)

The main result is: \(| x| <C_ mn^{1/m}\) implies \(w(x)p^ 2_ n(x)\leq C'n^{-1/m},\) \(n=0,1,2...\); where \(w(x)=\exp (-x^ m)\) for real x, and an even integer m, \(p_ n(x)\) is the normalized orthogonal polynomial of degree n for the weight function w, and C', \(C_ m\) are certain constants. Specifically, for any C with \(0<C<1\) there exists C' so that the inequality holds for \(C_ m=C(B(1/2,m/2))^{1/m},\) (the Beta function).