Asymptotic expansions of recursion coefficients of orthogonal polynomials with truncated exponential weights

Let beta > 0 and W-beta(x) = exp(-\x\(beta)), x is an element of R. For c > 0, define W-beta,(cn)(x) = W-beta(x) if \x\ less than or equal to c(1/beta) alpha(2n), and W-beta,(cn)(x) = 0 if \x\ > c(1/beta) alpha(2n), where alpha(2n) denotes Mhaskar-Rahmanov-Saff number for W-beta. Let gamma(n)(W-beta,W-cn) be the leading coefficient of the nth orthonormal polynomial corresponding to W-beta,W-cn and write alpha(n)(W-beta,W-cn) = gamma(n-1) (W-beta,W-cn)/gamma(n)(W-beta,W-cn). It is shown that if c > 1 and beta is a positive even integer then alpha(n)(W-beta,W-cn)/n(1/beta) has an asymptotic expansion. Also when 0 < c < 1, asymptotic expansions of recursion coefficients of the truncated Hermite weights are given.