Asymptotic behaviour of Stieltjes polynomials for ultraspherical weight functions

For the ultraspherical weight functions w_#lambda#(x) = (1 -x"2)"#lambda#"-"1"/"2, an asymptotic representation of the Stieltjes polynomials is proved for 1 < #lambda# #<=# 2, which holds uniformly in every closed subinterval of (-1,1). This extends and completes our earlier results (for 0 #<=##lambda##<=# 1) in the sense that the problem is solved for all ultraspherical weight functions for which Stieltjes polynomials are known to have only real distinct zeros inside (-1,1) for all n element of N. The main result is applied to prove positivity results for Kronrod extensions of Gauss and Lobatto quadrature formulae. (orig.)SIGLEAvailable from TIB Hannover: RO 8347(1994,3)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman