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Extension of “A multivariate convergence theorem of the “de Montessus de Ballore” type” to multipoles. (English) Zbl 0756.41023

Summary: We proved [ibid. 32, No. 1/2, 47-57 (1990; Zbl 0715.41023)] a multivariate version of the de Montessus de Ballore theorem stating the convergence of general order Padé approximants for multivariate meromorphic functions with so-called “simple” poles. That result is extended here to the case of “multipoles”.

MSC:

41A21 Padé approximation

Citations:

Zbl 0715.41023
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References:

[1] Cuyt, A., Multivariate Padé approximants revisited, BIT, 26, 71-79 (1986) · Zbl 0622.65011
[2] Cuyt, A., A multivariate convergence theorem of the “de Montessus de Ballore” type, J. Comput. Appl. Math., 32, 1&2, 47-57 (1990) · Zbl 0715.41023
[3] Gunning, R.; Rossi, H., Analytic Functions of Several Complex Variables (1965), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0141.08601
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