Generalized continued fraction expansions for pi and e

Kadyrov S., Mashurov F.

JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, vol.24, no.6, pp.1809-1819, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 6
  • Publication Date: 2021
  • Doi Number: 10.1080/09720529.2021.1936897
  • Journal Name: JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1809-1819
  • Keywords: Generalized continued fraction, pi, Euler number e, Ramanujan machine
  • Süleyman Demirel University Affiliated: No

Abstract

Recently Raayoni et al. announced various conjectures on continued fractions of fundamental constants automatically generated with machine learning techniques. in this paper, we prove some of their stated conjectures for Euler number e and show the equivalence of some of the listed conjectures. Moreover, we propose a simple method that can be used to generate other continued fractions using their series representations.