On the values of continued fractions: q-series

Abstract

Using the Poincare´-Perron theorem on the asymptotics of the solutions of linear recurrences it is proved that for a class of q-continued fractions the value of the continued fraction is given by a quotient of the solution and its q-shifted value of the corresponding qfunctional equation. r

On Diophantine approximations of Ramanujan type q-continued fractions

“…In the case (b), the assumption d > 0 implies |β| < |α|, too. Thus, by using the relation (28) we may apply Theorem 1 with the subsequent Observation 1 in order to get (14) and (15). 2…”

On Diophantine approximations of the solutions of q-functional equations

“…The case m = 2 has interesting implications for the values of certain q-continued fractions (see [10,12]). …”

“…are linearly independent over K (an algebraic number eld) having a linear independence measure depending on the degrees s, r i (i = 1; : : : ; m) and the dimension of the vector space generated by the numbers (1.3). The case m = 2 has interesting implications for the values of certain q-continued fractions (see [10,12]).…”