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The three main methods used in diophantine analysis of q-series are combined to obtain new upper bounds for irrationality measures of the values of the q-logarithm function
This new concept of continued fractional measure of irrationality for the real number a is introduced with the help of the classical measure of irrationality. Some relationships between this new and the classical measures are included. Acknowledgements. Supported by the grants no. 201/07/0191, ME09017 and MSM6198898701. 1991 Mathematics Subject… (More)
Using the Poincaré–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 2003 Elsevier Inc. All rights reserved.