Some new asymptotic properties for the zeros of Jacobi,Laguerre, and Hermite polynomials

For the generalized Jacobi, Laguerre, and Hermite polynomials $P_n^{left( {alpha _n ,beta _n } right)} left( x right),L_n^{left( {alpha _n } right)} left( x right),H_n^{left( {gamma _n } right)} left( x right)$ , the limit distributions of the zeros are found, when the sequences α _n or β _n tend to infinity with a larger order thann. The derivation uses special properties of the sequences in the corresponding recurrence formulas. The results are used to give second-order approximations for the largest and smallest zero which improve (and generalize) the limit statements in a paper by Moak, Saff, and Varga [11].