A UNIFIED CONTINUED FRACTION EXPANSION AND INDEPENDENCE CHARACTERIZATION

Abstract

 An algorithm to construct a general continued fraction expansion for
 elements in a discrete-valued non-archimedean fields (K,|·|) is devised.
 Such continued fraction takes the form
 b1
 a1+
 b2
 a2+ ··· bn
 an+ ··· ,
 where the elements an,bn are subject to the condition |an| > |bn|. Sev
eral examples are given to show that this algorithm yields almost all
 known continued fraction expansions as special cases. Criteria for alge
braic and linear dependences of certain classes of such continued fractions
 are derived.