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A World Record-Breaking Formula For pi: Hyper Accelerated Convergence
Subject area: Science,Engineering and Technology · Area of research: Find the value of "pi"
Abstract
I present a novel infinite series representation for ?\pi, which achieves unprecedented convergence speed: approximately one million digits of correct precision after just the first two terms of the series. The formula is based on an intricate factorial ratio combined with a large exponential decay factor and a linear polynomial coefficient. I provide theoretical motivation, derive the key parameters, analyze convergence properties rigorously, and benchmark the formula against classical ? series including Chudnovsky and Ramanujan-type formulas. The formula marks a new frontier in the efficient computation of ?\pi, with potential implications for numerical analysis, high-precision arithmetic, and computational mathematics.
How to cite this paper
@article{1709323,
author = {Samprit Sarkar},
title = {A World Record-Breaking Formula For pi: Hyper Accelerated Convergence},
journal = {Iconic Research And Engineering Journals},
year = {2025},
volume = {8},
number = {12},
pages = {1228-1231},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1709323.pdf},
abstract = {I present a novel infinite series representation for ?\pi, which achieves unprecedented convergence speed: approximately one million digits of correct precision after just the first two terms of the series. The formula is based on an intricate factorial ratio combined with a large exponential decay factor and a linear polynomial coefficient. I provide theoretical motivation, derive the key parameters, analyze convergence properties rigorously, and benchmark the formula against classical ? series including Chudnovsky and Ramanujan-type formulas. The formula marks a new frontier in the efficient computation of ?\pi, with potential implications for numerical analysis, high-precision arithmetic, and computational mathematics.},
month = {June},
}