The convergence of diagonal Pade approximants and the Pade conjecture

[摘要] Questions related to the convergence problem of diagonal Pade approximants are discussed. A central place is taken by the Pade 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 Pade Conjecture is analyzed.

[发布日期] 1997-11-28

[关键词] Pade approximation;Baker-Gammel-Wills conjecture;Pade Conjecture;convergence in capacity;spurious poles