International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 4, Pages 793-796

Approximation of the semi-infinite interval

A. McD. Mercer

Department of Mathematics and Statistics, University of Guelph, Ontario, Guelph, Canada

Received 11 February 1980

Copyright © 1980 A. McD. Mercer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The approximation of a function fC[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,) based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αeuxk=N(ux)kα+β1Γ(kα+β)f(kαu)The present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.