Zeros of Padé approximants for some classes of functions

• Autorzy: Ralitza K. Kovacheva
• Języki publikacji: EN

Abstrakty

EN

In the present paper, we deal with functions $f(z) := ∑_{n=0}^{∞} a_{n} z^{n}$ whose coefficients satisfy a special smoothness condition. Theorems concerning the asymptotic behaviour as $ → ∞, m - fixed, of the normalized in an appropriate way Padé approximants $π_{n,m}$ are provided. As a consequence, results concerning the limiting distribution of the zeros are deduced.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 37
• Numer: 1
• Strony: 243-250

Daty

wydano

1996

Twórcy

autor

Ralitza K. Kovacheva

• Institute of Mathematics, Bulgarian Academy of Sciences, BG-1090 Sofia, Bulgaria

Bibliografia

• [1] G. A. Baker, Essentials of Padé Approximants, Academic Press, New York, 1975.
• [2] A. Edrei, E. B. Saff and R. S. Varga, Zeros of Sections of Power Series, Springer Verlag, Lecture Notes in Mathematics, Vol. 1002, Berlin, 1983.
• [3] R. K. Kovacheva and E. B. Saff (1993), Zeros of Padé Approximants for Entire Functions with Smooth Maclaurin Coefficients, to appear in J. of Approx. Th. (1993).
• [4] D. S. Lubinsky, Uniform Convergence of Rows of Padé Table for Functions with Smooth Maclaurin Coefficients, Constr. Approx. 3 (1987), 307-330.
• [5] O. Perron, Die Lehre von den Kettenbruechen, 3rd ed., Chelsea Pub., New York, 1957.
• [6] E. B. Saff and R. S. Varga, On Zeros and Poles of Padé Approximants to $e^z$, Numer. Math. 25 (1975), 1-14.