Work

Sharp Arcsine-Type Bounds and Analytic Approximations for the Gauss Lemniscate Sine Function

Year: 2026

Type: article

Abstract: This paper develops two novel arcsine-type analytic approximation formulas for arcsl(x), the Gauss lemniscate sine function, each equipped with a monotonic and bounded remainder term of order x29 as x→0, which demonstrates the high accuracy of the obtained formulas near the origin. Based on these approximations, we establish several new sharp inequalities valid on the interval (0,1). Numerical evidence confirms that the resulting bounds provide improved accuracy compared with existing estimates in the literature, particularly in a neighborhood of the origin.

Source: Mathematics

DOI: 10.3390/math14111898

Authors: Mansour Mahmoud, Hanan Almuashi, Cristinel Mortici

Institutions: King Abdulaziz University, University of Jeddah, Academia Oamenilor de Știință din România, Valahia University of Targoviste, Universitatea Națională de Știință și Tehnologie Politehnica București

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: King Abdulaziz University