Abstract. Explicit formulas for Cotes numbers of the generalized Gaussian Hermite quadrature formula based on the zeros of the $n$-th Chebyshev polynomial and their asymptotic behavior as $n\to\infty $ are given. This provides a solution of a modification of Problem 26 of P. Turán [J. Approximation Theory, 29 (1980), 23-85].

AMS Subject Classification (1991): 41A55, 65D32

Received January 25, 1995. (Registered under 5686/2009.)