Simpler than the Nuttall--Pommerenke theorem is an earlier theorem of de Montessus de Ballore, concerning rows of the Pade table rather than diagonals, which asserts that as m [right arrow] [infinity] with fixed n, the poles of approximants [r.
The limit N [right arrow] [infinity] and an analogue of the Pade table.
mn] is the type (m, n) approximation to a fixed function f determined in this way, then we may imagine a table of approximations to f, analogous to the usual Pade table, with m displayed horizontally and n vertically.
The investigations in  -  deal with Padd approximants in the whole Pade table.
In  not only diagonal sequences, but the whole range of non-diagonal ray sequences of Pade polynomials has been studied, and among other very interesting results it has been shown how the asymptotic cluster sets of the zeros of non-diagonal Pade polynomials continuously change with the angle of the ray sequences in the Pade table.
JAGER, A multidimensional generalisation of the Pade table, proc.