Certain continued fractions associated with the Pad� table

Continued fractions associated with the Newton-Pad� table

“…The case of fully confluent interpolation points, i.e., the Pad6 case, is not excluded. In this latter case the continued fraction constructed for the block diagonal sequence is equivalent (but not identical) to a Magnus P-fraction [13]. A modification of the algorithm for avoiding infinite interpolation values would easily lead to Arndt's generalization of Werner's algorithm [1].…”

“…Another variant of the algorithm yields a fraction whose convergents are the entries on one diagonal. (In this case, the fraction is a generalization of a Magnus P-fraction [13,14].) In Sect.…”

Ergodic properties of some inverse polynomial series expansions of laurent series

“…In a partly parallel way, Artin [1] and Magnus [9,10] had earlier studied a Laurent series analogue of simple continued fractions of real numbers, involving "digits" Xl,Z2,... in a polynomial ring as above. In addition to sketching elementary properties of an n-dimensional "Jacobi-Perron" variant of this, Paysant-Leroux and Dubois [11,12] also briefly outlined certain "metric" theorems analogous to some of Khintchine [7] for real continued fractions, in the case when F is a finite field.…”

A theorem on $T$-fractions corresponding to a rational function

“…For some types of continued fractions corresponding formally to power series, the C-and P-fractions [3], [4], an analogue result is known: They are both terminating if and only if the power series expansion is the expansion of a rational function. But contrary to these fractions, the P-fractions are nonterminating by definition, which seems to make the question of rationality rather complicated.…”