Automatic conjecturing and proving of exact values of some infinite families of infinite continued fractions

Robert Dougherty-Bliss, Doron Zeilberger

Research output: Contribution to journalArticlepeer-review

Abstract

Inspired by the recent pioneering work, dubbed “The Ramanujan Machine” by Raayoni et al. (The Ramanujan Machine: Automatically Generated Conjectures on Fundamental Constants. arXiv preprint. arXiv:1907.00205, 2019), we (automatically) [rigorously] prove some of their conjectures regarding the exact values of some specific infinite continued fractions, and generalize them to evaluate infinite families (naturally generalizing theirs). Our work complements their beautiful approach, since we use symbolic rather than numeric computations, and we instruct the computer to not only discover such evaluations, but at the same time to prove them rigorously.

Original languageEnglish (US)
JournalRamanujan Journal
DOIs
StateAccepted/In press - 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Computer algebra
  • Continued fractions
  • Experimental mathematics

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