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, 1998
 
ISSN 



10197168
 
Volume/pages 



10:1(1998), p. 2949
 
ISI 



000078510400002
 
