Padé tables of entire functions of very slow and smooth growth (Q1078446)

The author proves normality of the Padé table for a class of entire functions f satisfying growth conditions on the coefficients; furthermore it is shown that the sequences of approximants \(L/M_ L\), with \((M_ L)\) an arbitrary sequence of denominator degrees, converge uniformly to f on compact subsets of the complex plane (i.e. the main diagonal converges!). The simple part of the proof uses another paper by the author [Proc. Am. Math. Soc. 94, 399-405 (1985; Zbl 0572.30032)] and the hard part is given in its ''complete'' form: an interesting and well organized paper.