The first aim of this paper is to investigate the growth of the entire function defined by the Laplace-Stieltjes transform converges on the whole complex plane. By introducing the concept of generalized order, we obtain two equivalence theorems of Laplace-Stieltjes transforms related to the generalized order, A ^*_n and λ_n. The second purpose of this paper is to study the problem on the approximation of this Laplace-Stieltjes transform. We also obtain some theorems about the generalized order, the error, and the coefficients of Laplace-Stieltjes transforms, which are generalization and improvement of the previous results.

中文翻译：

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关于近似和广义阶的Laplace-Stieltjes变换表示的整个函数

本文的首要目的是研究由Laplace-Stieltjes变换定义的整个函数的增长在整个复杂平面上收敛。通过引入广义顺序的概念，我们获得与广义次序，A拉普拉斯变换Stieltjes两个等价定理^* _Ñ和λ _Ñ。本文的第二个目的是研究有关Laplace-Stieltjes变换的逼近问题。我们还获得了有关广义阶，误差和Laplace-Stieltjes变换的系数的一些定理，这些定理是对先前结果的概括和改进。