A. McD. Mercer, "Approximation of the semi-infinite interval", International Journal of Mathematics and Mathematical Sciences, vol. 3, Article ID 891468, 4 pages, 1980. https://doi.org/10.1155/S0161171280000580
Approximation of the semi-infinite interval
The approximation of a function 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 based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is The present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.
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