STUDY ON MEAN VALUES OF AN ENTIRE FUNCTION AND ITS DERIVATIVES
By
Praneeta Verma¹ and Anil Kumar²
¹Department of Mathematics, Starex University, Gurgaon, Haryana,India-122413
²Department of Applied Science and Humanities (Mathematics), KCC Institute of Technology and Management, Knowledge Park-III, Greater Noida, Uttar Pradesh, India-20106
Email: pvpraneeta@gmail.com, dranilkumar73@rediffmail.com
(Received: September 04, 2023; In format: January 24, 2024; Revised: April 03; 2024; Accepted: April 12, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54122
Abstract
In this paper, we investigate mean values of an entire function and its derivative in the usual notation. It is obvious that generally λ1 ≤ λ and ρ1 ≤ ρ, Sugimura[12]there are entire Dirichlet’s series for which λ1 < λ and ρ1 < ρ. We have generally to distinguish between the limits as well as types of f(s) belonging to the same order ρ1 (0 < ρ1 < ∞) Bhan and Rastogi [1]We obtain some result of m2,k(σ) Kamthan [7]for the mean value of an entire Dirichlet’s series and its derivative. In this paper we shall establish some interesting results in term of theorems on mean values of an entire function and its derivatives.
2020 Mathematical Sciences Classification: 30D30, 11M32, 11M41.
Keywords and Phrases: Generalized order (ρ), Generalized lower order (λ), Type of the function (t), Lower type of function (t),Mean value I2(σ).