If 
is a power series which is regular for 
except for 
poles within this circle
and except for 
,
at which points the function is assumed continuous when only points 
are considered, then at least a subsequence of the
![[N,N]](/images/equations/PadeConjecture/Inline6.svg)
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 
for 
.
Padé Conjecture
See also
Padé ApproximantExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Padé ConjectureCite this as:
Weisstein, Eric W. "Padé Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PadeConjecture.html