On the asymptotics of the rows of the Padé table of analytic functions with logarithmic branch points

For the functions , where l n and a n are arithmetic progressions and their Padé approximants π n,m ( z; f ), we establish an asymptotics of the decrease of the difference f ( z ) − π n,m ( z; f ) for the case in which z ∈ D = { z : | z | < 1}, m is fixed, and n → ∞. In particular, we obtain proximate orders of decrease of best uniform rational approximations to the functions ln(1 − z ) and arctan z in the disk D q = { z : | z | ≤ q < 1}.