Padé Conjecture

If P(z) is a power series which is regular for |z|<=1 except for m poles within this circle and except for z=+1, at which points the function is assumed continuous when only points |z|<=1 are considered, then at least a subsequence of the [N,N] Padé approximants are uniformly bounded in the domain formed by removing the interiors of small circles with centers at these poles and uniformly continuous at z=+1 for |z|<=1.

See also

Padé Approximant

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Baker, G. A. Jr. "The Padé Conjecture and Some Consequences." §II.D in Advances in Theoretical Physics, Vol. 1 (Ed. K. A. Brueckner). New York: Academic Press, pp. 23-27, 1965.

Referenced on Wolfram|Alpha

Padé Conjecture

Cite this as:

Weisstein, Eric W. "Padé Conjecture." From MathWorld--A Wolfram Web Resource.

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