Sharp Bounds for the Arc Lemniscate Sine Function

2019/03/10 by Horst Alzer, Man Kam Kwong, Alzer, Horst +1
Mathematics · #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1903.03897

openalex publication_date 2019/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The arc lemniscate sine function is given by arcsl(x)=∫₀^x (1)/(√(1-t⁴))dt. In 2017, Mahmoud and Agarwal presented bounds for arcsl in terms of the Lerch zeta function Φ(z,s,a)=∑_k=0^∞ \frac z^k(k+a)^s. They proved (1)/(8) x Φ(x⁴, 3/2, 1/4) < arcsl(x)< (1)/(4) x Φ(x⁴,3/2,1/4) (0

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