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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 ln q (1 − z) = ∞ ν=1 z ν q ν 1 − q ν , |z| 1, when p = 1/q ∈ Z \ {0, ±1} and z ∈ Q.

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 q-functional equation.

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