Approximation of the semi-infinite interval

A. McD. Mercer

International Journal of Mathematics and Mathematical Sciences, 1980, vol. 3, 1-4

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 α e − u x ∑ k = N ∞ ( u x ) k α + β − 1 Γ ( k α + β ) f ( k α u ) The present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:891468

DOI: 10.1155/S0161171280000580

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