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Convergence of rows of the Pade table

Journal Article · · J. Math. Anal. Appl.; (United States)

It is proved that at least an infinite subsequence of (l/2) Pade approximants converge to f(z) if f(z) is holomorphic. It is speculated that convergence of the (L - m/..mu.. + m) approximants to c(z) is associated with convergence of (L/..mu..) approximants to h(z), where c(z) is meromorphic with ..mu.. poles and sigma(z) is the polynomial of degree ..mu.. which renders g(z) = sigma(z)c(z) and h(z) = sigma(z)g(z) holomorphic. This conjecture is formulated precisely and proved for m = 1 and m = 2 and h(z) a holomorphic function of order less than 1.

Research Organization:
Brookhaven National Lab., Upton, NY
OSTI ID:
7303681
Journal Information:
J. Math. Anal. Appl.; (United States), Journal Name: J. Math. Anal. Appl.; (United States) Vol. 57:2; ISSN JMANA
Country of Publication:
United States
Language:
English

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