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 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 Approximant## Explore 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 Conjecture## Cite this as:

Weisstein, Eric W. "Padé Conjecture."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/PadeConjecture.html