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Padé approximants in complex points revisited. (English) Zbl 1216.30037

Summary: The class of complex symmetric functions contains the Stieltjes functions. The aim of this work is to give some new results concerning the location of the zeros and poles of Padé approximants using the Taylor series of functions developed in neighborhoods of complex points and their conjugate points.

MSC:

30E10 Approximation in the complex plane
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References:

[1] J. S. R. Chisholm, A. C. Genz, and M. Pusterla, “A method for computing Feynman amplitudes with branch cuts,” Journal of Computational and Applied Mathematics, vol. 2, no. 2, pp. 73-76, 1976. · Zbl 0333.65053 · doi:10.1016/0771-050X(76)90010-3
[2] S. Klarsfeld, “Padé approximants and related methods for computing boundary values on cuts,” in Padé Approximation and Its Applications, vol. 888 of Lecture Notes in Mathematics, pp. 255-262, Springer, Berlin, Germany, 1981. · Zbl 0474.41005 · doi:10.1007/BFb0095591
[3] J. Gilewicz, Approximants de Padé, vol. 667 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1978. · Zbl 0378.30015
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