Explicit construction of general multivariate Padé approximants to an Appell function

Advances in Computational Mathematics

Volumn 22, Issue 3, 2005, Pages 249-273

  Borwein, P B ^a   Cuyt, A ^b   Zhou, P ^c  

^a SIMON FRASER UNIVERSITY   (Canada)

^b UNIVERSITY OF ANTWERP   (Belgium)

^c ST FRANCIS XAVIER UNIVERSITY   (Canada)

Author keywords

Hypergeometric function; Multivariate; Pad approximant

Indexed keywords

EID: 13844253861     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-003-2600-8     Document Type: Article

References (18)

1. H. Allouche and A. Cuyt, On the structure of a table of multivariate rational interpolants, Constr. Approx. 8 (1992) 69-86.
2. P.B. Borwein, Padé approximants for the q-elementary functions, Constr. Approx. 4 (1988) 391-402.
3. A. Cuyt, Multivariate Padé approximants revisited, BIT 26 (1986) 71-79.
4. A. Cuyt, How well can the concept of Padé approximant be generalized to the multivariate case? J. Comput. Appl. Math. 105 (1999) 25-50.
5. A. Cuyt, K. Driver and D. Lubinsky, Kronecker type theorems, normality and continuity of the multivariate Padé operator. Numer. Math. 73 (1006) 311-327.
6. A. Cuyt, K. Driver, J. Tan and B. Verdonk, Exploring multivariate Padé approximants for multiple hypergeometric series, Adv. Comput. Math. 10 (1999) 29-49.
7. A. Cuyt and B. Verdonk, General order Newton-Fade approximants for multivariate functions, Numer. Math. 43 (1985) 293-307.
8. M.G. de Bruin, Some classes of Padé tables whose upper halves are normal, Nieuw Archief Voor Wiskunde XXV(3) (1977) 148-160.
9. G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, Vol. 35 (Cambridge Univ. Press, Cambridge, 1990).
10. D.S. Lubinsky, Power series equivalent to rational functions: a shifting-origin Kronecker type theorem, and normality of Padé tables, Numer. Math. 54 (1988) 33-39.
11. H. Padé, Recherches sur la convergence des développements en fractions continues d'une certaine catégorie de fonctions, Ann. Sci. l'Ecole Normale Supérieure 24 (1907) 341-400.
12. L.J. Slater, Generalized Hypergeometric Functions (Cambridge Univ. Press, Cambridge, 1966).
13. H. van Rossum, Systems of orthogonal and quasi orthogonal polynomials connected with the Padé table II, Nederl. Akad. Wetensch. Proc. 58 (1955) 526-534.
14. H. Werner and E. Wuytack, On the continuity of the Padé operator, SIAM J. Numer. Anal. 20 (1983) 1273-1280.
15. P. Wynn, A general system of orthogonal polynomials, Quart. J. Math. Oxford 18 (1967) 81-96.
16. P. Zhou, Explicit construction of multivariate Padé approximants, J. Comput. Appl. Math. 79 (1997) 1-17.
17. P. Zhou, Multivariate Padé approximants associated with functional relations, J. Approx. Theory 93 (1998) 201-230.
18. P. Zhou, Explicit construction of multivariate Padé approximants for a q-logarithm function, J. Approx. Theory 103 (2000) 18-28.