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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