The Wallis-Catalan Infinite Product Formula and the Lemniscate Constant

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-06
DOI
https://doi.org/10.5281/zenodo.18854932
Primary Topic
Advanced Mathematical Identities
Type
preprint
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preprint

The Wallis-Catalan Infinite Product Formula and the Lemniscate Constant

Robert Joseph Andrew Bilinski
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Identities
preprint

The Wallis-Catalan Infinite Product Formula and the Lemniscate Constant

Robert Joseph Andrew Bilinski
preprint en

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.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Identities
DOIOpen Access PDFOpenAlex
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The Wallis-Catalan Infinite Product Formula and the Lemniscate Constant — Robert Joseph Andrew Bilinski · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS