The Wallis-Catalan Infinite Product Formula and the Lemniscate Constant | Synapse
May 14, 2026Open Access
The Wallis-Catalan Infinite Product Formula and the Lemniscate Constant
Key Points
The aim is to establish a connection between the Wallis product formula and the Catalan numbers, demonstrating its convergence to the Lemniscate constant.
Developed a Wallis-type product formula based on Catalan numbers.
Analyzed convergence properties of the product formula mathematically.
The product formula converges to ϖ/4, demonstrating a strong relationship with the Lemniscate constant.
Abstract
A Wallis-type product formula is established using the Catalan numbers. This is shown to converge to ϖ/4, a quarter of the Lemniscate constant.