Transcendence of Some Power Series in Function Fields

    Let $\Bbbk$ be a field of characteristic $0$.    Let $\Bbbk((1/x))$ be the function field with respect to the degree valuation $|\cdot|_\infty$. In this paper, we show that the values of some power series over $\Bbbk(x)$ evaluated at certain Liouville numbers in $\Bbbk((1/x))$ are either rational over $\Bbbk[x]$ or transcendental. Some examples are also included.