Growth and approximation of Laplace-Stieltjes transform with \((p, q)\)-proximate order converges on the whole plane (Q2305198)

The authors introduce the concept of \((p,q)\)-proximate order of a Laplace-Stieltjes transform to investigate the growth and approximation of entire functions represented by Laplace-Stieltjes transforms. An equivalence theorem of the \((p,q)\)-proximate order of Laplace-Stieltjes transforms is obtained. They study the approximation of entire functions defined by a Laplace-Stieltjes transform with \((p,q)\)-proximate order. Furthermore, some results about the \((p,q)\)-proximate order, the error, and the coefficients of Laplace-Stieltjes transforms are obtained.