A High-Precision Approximation to PI using a Hyperbolic Convergence Sequence

This note presents a hyperbolic convergence to PI based on the nested relationship between the standard inverse tangent and the hyperbolic tangent functions.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-05
DOI
https://doi.org/10.5281/zenodo.23990480
Primary Topic
Advanced Mathematical Identities
Type
preprint
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preprint

A High-Precision Approximation to PI using a Hyperbolic Convergence Sequence

Bheema Varanasi
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Identities
preprint

A High-Precision Approximation to PI using a Hyperbolic Convergence Sequence

Bheema Varanasi
preprint en

Abstract

This note presents a hyperbolic convergence to PI based on the nested relationship between the standard inverse tangent and the hyperbolic tangent functions.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Identities
DOIOpen Access PDFOpenAlex
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A High-Precision Approximation to PI using a Hyperbolic Convergence Sequence — Bheema Varanasi · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS