On the Approximation of an Analytic Function Represented by Laplace-Stieltjes Transformation

Abstract

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,\beta } )$ where $ {E_n}( {F,\beta } )$ is the error in approximating of the function $F(s)$  by definite integral polynomials in the half plane $ {{Re}} s \le \beta  < \alpha. $