**Generalizations**

A formal Newton series *L* is of the form

where the sequence {β_{k}} of points in the complex plane is known as the set of *interpolation points*. A sequence of rational approximants *R _{m,n}* can be formed for such a series

*L*in a manner entirely analogous to the procedure described above, and the approximants can be arranged in a

*Newton-Padé table*. It has been shown that some "staircase" sequences in the Newton-Padé table correspond with the successive convergents of a Thiele-type continued fraction, which is of the form

Mathematicians have also constructed *two-point Padé tables* by considering two series, one in powers of *z*, the other in powers of 1/*z*, which alternately represent the function *f*(*z*) in a neighborhood of zero and in a neighborhood of infinity.

Read more about this topic: Padé Table