Padé table

Summary

The Padé table of a power series is the array of all its Padé approximants $[m/n]$. It is indexed by the numerator degree $m$ and the denominator degree $n$. Its first column holds the Taylor polynomials, and its diagonal holds the diagonal approximants $[n/n]$. Equal entries occur in square blocks, and the table is called normal when every entry occurs only once. The table organizes convergence questions and links Padé approximants with continued fractions.