Transcendental Continued Fractions
Sarra Ahallal, Ali Kacha

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 and that will assure us that the continued fraction is a transcendental number. With the same condition, we establish a transcendental measure of
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Taxonomy
TopicsMathematical Dynamics and Fractals · Mathematical and Theoretical Analysis · History and Theory of Mathematics
