GENERALIZED CONTINUED FRACTION EXPANSION FOR EULER CONSTANT

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Date

2021

Journal Title

Journal ISSN

Volume Title

Publisher

СДУ хабаршысы - 2021

Abstract

Abstract. The theory of continued fractions is one of the oldest fields of number theory going back as far as Euclid 300 BCE. As opposed to generalized continued fractions, the theory of simple continued fractions is well-developed and finds many applications in various fields. In this article we consider a problem of elegant representations of famous mathematical constants with generalized continued fraction and prove that the Euler constant e satisfies the generalized continued fraction formula This is one of the conjectures generated in www.RamanujanMachine.com using machine learning techniques. Our method of proof uses only elementary techniques.

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Keywords

Generalized Continued Fraction, Euler number e, Ramanujan Machine, Number theory, СДУ хабаршысы - 2021, №1

Citation

G. Turgynbai / GENERALIZED CONTINUED FRACTION EXPANSION FOR EULER CONSTANT / СДУ хабаршысы - 2021