Abstract
Abstract In this study, we consider some power series with rational coefficients and investigate transcendence of the values of these series for Liouville number arguments. It is proved that these values are either a Liouville number or a rational number under certain conditions. AMS Subject Classification:11J81, 11J17.
Highlights
A real number α is algebraic if it is a zero of a polynomial with integer coefficients
The development of the theory of transcendental numbers has proved to have a strong influence on some new studies in Diophantine equations; see [, ]
A classification of the set of all transcendental numbers into three disjoint classes, termed S, T and U, which was introduced by Mahler [ ], proved to be of considerable value in the general development of the subject
Summary
1 Introduction A real number α is algebraic if it is a zero of a polynomial with integer coefficients. The real numbers which are not algebraic are known as transcendental. It follows from this that almost all real numbers are transcendental.
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