Title
Exploring multivariate Padé approximants for multiple hypergeometric series Exploring multivariate Padé approximants for multiple hypergeometric series
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Basel :Baltzer ,
Subject
Mathematics
Source (journal)
Advances in computational mathematics. - Basel
Volume/pages
10(1998) :1 , p. 29-49
ISSN
1019-7168
ISI
000078510400002
Carrier
E
Target language
English (eng)
Affiliation
University of Antwerp
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.
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