Padé Conjecture

If $P(z)$ is a Power series which is regular for $\vert z\vert\leq 1$ except for $m$ Poles within this Circle and except for $z=+1$, at which points the function is assumed continuous when only points $\vert z\vert\leq 1$ 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 $\vert z\vert\leq 1$.

See also Padé Approximant

References

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.