The Approximation of Laplace-Stieltjes Transforms in the Half Plane

# Gyan Prakash Rathore1 and Anupma Rastogi1

1Department of Mathematics and Astronomy, Lucknow University, Lucknow, Uttar Pradesh, India.

Abstract: In this paper, we study the growth of the analytic function represented by Laplace-Stieltjes transform of infinite order which is convergent in the right half plane. We also investigate the error in approximation defined on Laplace-Stieltjes transform of finite $\gamma_{U}$-order in the half plane, and some relations between the error and growth of Laplace-Stieltjes transform of finite $\gamma_{U}$-order.
Keywords: Growth, Laplace-Stieltjes transform, approximation, $\gamma_{U}$-order.

Cite this article as: Gyan Prakash Rathore and Anupma Rastogi, The Approximation of Laplace-Stieltjes Transforms in the Half Plane, Int. J. Math. And Appl., vol. 9, no. 2, 2021, pp. 27-37.

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