Abstract. We study the rate of pointwise convergence for a sequence of positive linear operators $R_n^{[\beta ]}$ approximating functions on the infinite interval $[0,\infty )$ which were investigated by K. Balázs and Szabados. They are a special case of more general operators introduced by K. Balázs. The paper presents the complete asymptotic expansion for operators $R_{n}^{\left[ \beta\right ] }$ as $n$ tends to infinity. All coefficients are calculated explicitly. It turns out that Stirling numbers of first and second kind play an important role. Our work generalizes previous results.

AMS Subject Classification (1991): 41A25, 41A36, 41A60

Received October 20, 1998, and in revised form June 2, 1999. (Registered under 2726/2009.)