Upper bounds for the length of SEL Egyptian fraction expansions for rational elements of certain discrete-valued non-archimedean fields

Let K be a complete discrete-valued non-archimedean field. In the authors earlier work, the SEL Egyptian fraction expansion for elements of K was constructed, and characterizations of rational functions in the particular case of function fields, 𝔽((p(x))) and 𝔽((1/x)) were also established, where p(x) is an irreducible polynomial over a field 𝔽. One such characterizationstates that under a certain condition, the SEL Egyptian fraction expansion is finite if and only if it represents a rational function. In this paper, we obtain upper bounds for the length of finite SEL Egyptian fraction expansions for rational functions in the function fields 𝔽((x)) and 𝔽((1/x)). In the case of the p-adic number field ℚ p , it is shown that under a certain condition, a p-adic SEL Egyptian fraction expansion is finite if and only if it represents a rational number. An upper bound for the length of such expansions for rational numbers is also derived.