“…Independently, J.-P. Bézivin [3] in 1988 and P. Borwein [7] in 1991 pushed forward different analytical methods to establish the irrationality of the series for rational z and q of the form q = 1/p with p ∈ Z \ {0, ±1}, though Bézivin's paper did not mention L q (z) specifically -it was observed only later [9] that the general results from [3] imply the irrationality. The advantage of Borwein's method [7,8], in which he uses the Padé approximations to (2), is that it allows one to "measure" the irrationality of the numbers in question; this quantitative counterpart is absent in Erdős' method [18] and it was also absent in Bézivin's original method [3,4] until the recent work [30] of I. Rochev (see [31] for a further development). The Padé approximation technique as originated in [7,8] was significantly generalized and extended in later works (for example, [1,9,10,11,12,13,17,22,24,25,32,34,36,37] to list a few) to sharpen the irrationality measures of the values of q-harmonic and qlogarithm series as well as to prove the irrationality and linear independence results for some close relatives of the series.…”