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The convergence of diagonal Padé approximants and the Padé Conjecture

✍ Scribed by Herbert Stahl

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
695 KB
Volume
86
Category
Article
ISSN
0377-0427

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✦ Synopsis

Questions related to the convergence problem of diagonal Pad6 approximants are discussed. A central place is taken by the Pad6 Conjecture (also known as the Baker-Gammel-Wills Conjecture). Partial results concerning this conjecture are reviewed and weaker and more special versions of the conjecture are formulated and their plausibility is investigated. Great emphasis is given to the role of spurious poles of the approximants. A conjecture by Nuttall (1970) about the number and distribution of such poles is stated and its importance for the Pad~ Conjecture is analyzed.

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