International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 4, Pages 793-796
doi:10.1155/S0161171280000580
Approximation of the semi-infinite interval
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.
Abstract
The approximation of a function f∈C[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 αe−ux∑k=N∞(ux)kα+β−1Γ(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.