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
2026-05-12
DOI
https://doi.org/10.5281/zenodo.20145147
Primary Topic
Advanced Mathematical Identities
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

The Wallis-Catalan Infinite Product Formula and the Lemniscate Constant

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

The Wallis-Catalan Infinite Product Formula and the Lemniscate Constant

Robert 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
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

The Wallis-Catalan Infinite Product Formula and the Lemniscate Constant — Robert Bilinski · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS