THE APPROXIMATION ON ANALYTIC FUNCTION OF LAPLACE-STIELTJES TRANSFORMS WITH PROXIMATE ORDER CONSUMPTION
By
Gyan Prakash Rathore1, Anupma Rastogi2 and Deepak Gupta3
1Department of Mathematics, Sri Ramswaroop Memorial College of Engineering & Management, Lucknow, Uttar Pradesh, India-226028
2Department of Mathematics and Astronomy, University of Lucknow, Lucknow, Uttar Pradesh, India-226007
3Department of Mathematics, Faculty of Engineering and Technology, University of Lucknow, Uttar Pradesh, India - 226007
Email: gyan.rathore1@gmail.com, anupmarastogi13121993@gmail.com, dg61279@gmail.com
(Received: July 24, 2024; In format: January 18, 2025; Revised: September 21, 2025; Accepted: September 22, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55203
Abstract
In this paper, we investigate the growth of Mu(σ, F) defined by Laplace-Stieltjes transforms of proximate order which is convergent in the half plane. We obtain the error in approximating LaplaceStieltjes transform of finite order in the half plane by Dirichlet polynomials.
2020 Mathematical Sciences Classification: 44A10, 30D15.
Keywords and Phrases: Growth, Dirichlet series, order, approximation, analytic function, error.