The behaviours of convergents in theta-expansions: computational insights based on theta-expansions algorithm using the Maple software
Continued fractions arise naturally in long division and the theory of the approximation to real numbers by rational numbers. This research considered the implementation on the convergent of $\theta$-expansions of real numbers of $x\in(0,\theta)$ with $0<\theta<1$. The convergent of $\theta$-expansions are also called as $\theta$-convergent of continued fraction expansions. This study aimed to establish the properties for a family of $\theta$-convergent in $\theta$-expansions. The idea of discovering the behaviours of $\theta$-convergent evolved from the conce