Interesting Esoterica

A catalogue of mathematical formulas involving π, with analysis

Article by David H. Bailey
  • Published in 2020
  • Added on
This paper presents a catalogue of mathematical formulas and iterative algorithms for evaluating the mathematical constant π, ranging from Archimedes’ 2200-year-old iteration to some formulas that were discovered only in the past few decades. Computer implementations and timing results for these formulas and algorithms are also included. In particular, timings are presented for evaluations of various infinite series formulas to approximately 10,000-digit precision, for evaluations of various integral formulas to approximately 4,000-digit precision, and for evaluations of several iterative algorithms to approximately 100,000-digit precision, all based on carefully designed comparative computer runs.

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BibTeX entry

@article{ACatalogueOfMathematicalFormulasInvolvingPiWithAnalysis,
	title = {A catalogue of mathematical formulas involving π, with analysis},
	abstract = {This paper presents a catalogue of mathematical formulas and iterative algorithms for evaluating the mathematical constant π, ranging from Archimedes’ 2200-year-old iteration to some formulas that were discovered only in the past few decades. Computer implementations and timing results for these formulas and algorithms are also included. In particular, timings are presented for evaluations of various infinite series formulas to approximately 10,000-digit precision, for evaluations of various integral formulas to approximately 4,000-digit precision, and for evaluations of several iterative algorithms to approximately 100,000-digit precision, all based on carefully designed comparative computer runs.},
	url = {https://www.davidhbailey.com/dhbpapers/pi-formulas.pdf},
	year = 2020,
	author = {David H. Bailey},
	comment = {},
	urldate = {2020-03-27},
	collections = {Basically computer science,History,Lists and catalogues}
}