On the Approximation of an Analytic Function Represented by Laplace-Stieltjes Transformation (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 \le β < α. $
Keywords: Laplace-Stieltjes transformation; analytic function; order; type; approximation error.