What question did this study set out to answer?

The aim is to establish a connection between the Wallis product formula and the Catalan numbers, demonstrating its convergence to the Lemniscate constant.

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.

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Cite This Study

Robert Bilinski (Tue,) studied this question.

synapsesocial.com/papers/6a056751a550a87e60a1f536 https://doi.org/https://doi.org/10.5281/zenodo.20145147

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