Criteria for independence, both algebraic and linear, are derived for continued fraction expansions of elements in the field
of Laurent series. These criteria are then applied to examples involving elements recently discovered to have explicit series
and continued fraction expansions.
Authors:Pakwan Riyapan, Vichian Laohakosol and Tuangrat Chaichana
Two types of explicit continued fractions are presented. The continued fractions of the first type include those discovered
by Shallit in 1979 and 1982, which were later generalized by Pethő. They are further extended here using Peth\H o's method.
The continued fractions of the second type include those whose partial denominators form an arithmetic progression as expounded
by Lehmer in 1973. We give here another derivation based on a modification of Komatsu's method and derive its generalization.
Similar results are also established for continued fractions in the field of formal series over a finite base field.