(untitled) (Analysis in Theory and Applications, 2017)
In the present paper, we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of E_n( F,β ) where E_n( F,β ) is the error in approximating of the function F(s) by definite integral polynomials in the half plane Re s β < α.