Transcendental Continued Fractions

TL;DR

This paper provides conditions under which the exponential of a continued fraction is transcendental and establishes a measure for its transcendence, advancing understanding of transcendental numbers in continued fractions.

Contribution

It introduces specific conditions on continued fractions that guarantee the transcendence of their exponential, a novel result in transcendental number theory.

Findings

Conditions for transcendence of A^B established

Transcendental measure for A^B derived

Advances in understanding continued fractions and transcendental numbers

Abstract

In the present paper, we give sufficient conditions on the elements of the continued fractions $A$ and $B$ that will assure us that the continued fraction $A^B$ is a transcendental number. With the same condition, we establish a transcendental measure of $A^B.$