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1709323PublishedVol 8 · Issue 12

A World Record-Breaking Formula For pi: Hyper Accelerated Convergence

Samprit Sarkar

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

Samprit Sarkar "A World Record-Breaking Formula For pi: Hyper Accelerated Convergence" Iconic Research And Engineering Journals Volume 8 Issue 12 2025 Page 1228-1231
Samprit Sarkar "A World Record-Breaking Formula For pi: Hyper Accelerated Convergence" Iconic Research And Engineering Journals, vol. 8, no. 12, Jun. 2025
Samprit Sarkar (2025). A World Record-Breaking Formula For pi: Hyper Accelerated Convergence. Iconic Research And Engineering Journals, 8(12).
Samprit Sarkar "A World Record-Breaking Formula For pi: Hyper Accelerated Convergence" Iconic Research And Engineering Journals, vol. 8, no. 12, Jun. 2025.
@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},
  }