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The approximation of Laplace-Stieltjes transforms with finite order
Hong Yan Xu1,2, San Yan Liu1
1School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi 710126 China.
Abstract:
In this paper, we study the irregular growth of an entire function defined by the Laplace-Stieltjes transform of finite order convergent in the whole complex plane and obtain some results about λ-lower type. In addition, we also investigate the problem on the error in approximating entire functions defined by the Laplace-Stieltjes transforms. Some results about the irregular growth, the error, and the coefficients of Laplace-Stieltjes transforms are obtained; they are generalization and improvement of the previous conclusions given by Luo and Kong, Singhal and Srivastava.
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