Padé tables of a class of entire functions

Author:
D. S. Lubinsky

Journal:
Proc. Amer. Math. Soc. **94** (1985), 399-405

MSC:
Primary 30E10; Secondary 41A21

DOI:
https://doi.org/10.1090/S0002-9939-1985-0787881-9

MathSciNet review:
787881

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Abstract: It is shown that if the Maclaurin series coefficients of an entire function satisfy a certain explicit condition, then there exists a sequence of integers such that locally uniformly in as , for all nonnegative integer sequences . In particular, this condition is satisfied if the approach 0 fast enough, or if a subsequence of the behaves irregularly in a certain sense. Further, the functions satisfying this condition are dense in the space of entire functions with the topology of locally uniform convergence. Consequently, the set of entire functions satisfying the Baker-Gammel-Wills Conjecture is of the second category.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0787881-9

Keywords:
Padé approximation,
entire functions,
uniform convergence

Article copyright:
© Copyright 1985
American Mathematical Society