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 Fi, i = 1,..., 4, by multivariate Pade approximants. Section 1 reviews the results that exist for the projection of the Fi onto x = 0 or y = 0, namely, the Gauss function F2(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 F1( 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
,
1999
 
ISSN




10197168
 
Volume/pages




10
:1
(1998)
, p. 2949
 
ISI




000078510400002
 
