Name
Title | ||
|---|---|---|
Explicit construction of general multivariate Padé approximants to an Appell function |
Abstract | ||
|---|---|---|
Properties of Padé approximants to the Gauss hypergeometric function 2F1(a,b;c;z) have been studied in several papers and some of these properties have been generalized to several variables in [6]. In this paper we derive explicit formulae for the general multivariate Padé approximants to the Appell function F1(a,1,1;a+1;x,y)=?i,j=08(axiyj/(i+j+a)), where a is a positive integer. In particular, we prove that the denominator of the constructed approximant of partial degree n in x and y is given by
$q(x,y)=(-1)^{n}{{m+n+a}\choose n}F_{1}(-m-a,-n,-n;-m-n-a;x,y)$
, where the integer m, which defines the degree of the numerator, satisfies m=n+1 and m+a=2n. This formula generalizes the univariate explicit form for the Padé denominator of 2F1(a,1;c;z), which holds for c>a>0 and only in half of the Padé table. From the explicit formulae for the general multivariate Padé approximants, we can deduce the normality of a particular multivariate Padé table. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1007/s10444-003-2600-8 | Adv. Comput. Math. |
Keywords | Field | DocType |
Padé approximant,hypergeometric function,multivariate | Hypergeometric function,Integer,Explicit formulae,Padé table,Padé approximant,Mathematical analysis,Multivariate statistics,Univariate,Fraction (mathematics),Mathematics | Journal |
Volume | Issue | ISSN |
22 | 3 | 1019-7168 |
Citations | PageRank | References |
1 | 0.71 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Peter B. Borwein | 1 | 71 | 18.23 |
| Annie Cuyt | 2 | 161 | 41.48 |
| Ping Zhou | 3 | 5 | 2.61 |