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 $\lambda_n$. 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.
Hongyan XU
,
Yinying KONG
. ENTIRE FUNCTIONS REPRESENTED BY LAPLACE-STIELTJES TRANSFORMS CONCERNING THE APPROXIMATION AND GENERALIZED ORDER[J]. Acta mathematica scientia, Series B, 2021
, 41(2)
: 646
-656
.
DOI: 10.1007/s10473-021-0222-1
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