TY - JOUR T1 - On the Approximation of an Analytic Function Represented by Laplace-Stieltjes Transformation JO - Analysis in Theory and Applications VL - 4 SP - 407 EP - 420 PY - 2017 DA - 2017/10 SN - 31 DO - http://doi.org/10.4208/ata.2015.v31.n4.6 UR - https://global-sci.org/intro/article_detail/ata/4648.html KW - Laplace-Stieltjes transformation, analytic function, order, type, approximation error. AB -

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. $