Pade approximants for entire functions with regularly decreasing Taylor coefficients

Journal Article · Thu Oct 31 04:00:00 EST 2002 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2002V193N09ABEH000679; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21205720

Rusak, V N; Starovoitov, A P ^[1]

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1. Belarusian State University, Minsk (Belarus)

For a class of entire functions the asymptotic behaviour of the Hadamard determinants D{sub n,m} as 0{<=}m{<=}m(n){yields}{infinity} and n{yields}{infinity} is described. This enables one to study the behaviour of parabolic sequences from Pade and Chebyshev tables for many individual entire functions. The central result of the paper is as follows: for some sequences {l_brace}(n,m(n)){r_brace} in certain classes of entire functions (with regular Taylor coefficients) the Pade approximants {l_brace}{pi}{sub n,m(n)}{r_brace}, which provide the locally best possible rational approximations, converge to the given function uniformly on the compact set D={l_brace}z:|z|{<=}1{r_brace} with asymptotically best rate.

• OSTI ID: 21205720
• Journal Information: Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 9 Vol. 193; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
ASYMPTOTIC SOLUTIONS
FUNCTIONS