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  "body": "\n## Summary\n\nThe Padé table of a power series is the array of all its [[Padé approximants|1F16G4V64X]] $[m/n]$.\nIt is indexed by the numerator degree $m$ and the denominator degree $n$.\nIts first column holds the Taylor polynomials, and its diagonal holds the diagonal approximants $[n/n]$.\nEqual entries occur in square blocks, and the table is called normal when every entry occurs only once.\nThe table organizes convergence questions and links Padé approximants with [[continued fractions|04P2RJ4WPS]].\n\n## Explanations\n\n### L1 human\n\nFor a given function there is one best matching quotient of polynomials for each choice of the two degrees.\nWriting these quotients in a grid, by degree of the top and degree of the bottom, gives the Padé table.\nMoving down a column adds terms to the top; moving along a row allows more poles.\nFor $1/(1-z)$ every entry with a denominator of degree at least $1$ is $1/(1-z)$ itself, a single huge block.\n",
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