Publication
Title
Exploring multivariate Padé approximants for multiple hypergeometric series
Author
Abstract
We investigate the approximation of some hypergeometric functions of two variables, namely the Appell functions F-i, i = 1,..., 4, by multivariate Pade approximants. Section 1 reviews the results that exist for the projection of the F-i onto x = 0 or y = 0, namely, the Gauss function F-2(1)( a, b; c; z), since a great deal is known about Pade approximants for this hypergeometric series. Section 2 summarizes the definitions of both homogeneous and general multivariate Pade approximants. In section 3 we prove that the table of homogeneous multivariate Pade approximants is normal under similar conditions to those that hold in the univariate case. In contrast, in section 4, theorems are given which indicate that, already for the special case F-1( a, b, b'; c; x, y) with a = b = b' = 1 and c = 2, there is a high degree of degeneracy in the table of general multivariate Pade approximants. Section 5 presents some concluding remarks, highlighting the difference between the two types of multivariate Pade approximants in this context and discussing directions for future work.
Language
English
Source (journal)
Advances in computational mathematics. - Basel
Publication
Basel : Baltzer, 1998
ISSN
1019-7168
Volume/pages
10:1(1998), p. 29-49
ISI
000078510400002
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 08.10.2008
Last edited 07.11.2017
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