GENERALIZED CONTINUED FRACTION EXPANSION FOR EULER CONSTANT

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  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.