Approximation Of Logarithm, Factorial And Euler Mascheroni Constant Using Odd Harmonic Series

2025/11/26 by Narinder Kumar Wadhawan, Wadhawan, Narinder Kumar, Priyanka Wadhawan +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #FOS: Mathematics #Heat Transfer and Numerical Methods #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2511.21102

openalex publication_date 2025/11/26 · openalex created_date 2025/11/28 · openalex updated_date 2026/07/28

Abstract

We have proved in this paper that natural logarithm of consecutive number ratio, x/(x-1) approximates to 2/(2x - 1) where x is a real number except 1. Using this relation, we, then proved, x approximates to double the sum of odd harmonic series having first and last terms 1/3 and 1/(2x - 1) respectively. Thereafter, not limiting to consecutive number ratios, we extended its applicability to all the real numbers. Based on these relations, we, then derived a formula for approximating the value of Factorial x. We could also approximate the value of Euler-Mascheroni constant. In these derivations, we used only and only elementary functions, thus this paper is easily comprehensible to students and scholars.

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