Approximation of the semi-infinite interval - A. McD. Mercer (International Journal of Mathematics and Mathematical Sciences)
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.