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  "body": "\n## Definition\n\nLet $f(z) = \\sum_{k \\ge 0} c_k z^k$ be a [[formal power series|072W67KFYK]] with complex coefficients.\nFor integers $m, n \\ge 0$ let $[m/n]_f$ be the [[Padé approximant|75XCD68557]] of $f$ with numerator degree at most $m$ and denominator degree at most $n$.\nThe *Padé table* of $f$ is the doubly infinite array $\\big([m/n]_f\\big)_{m, n \\ge 0}$.\nThe table is *normal* if no rational function occurs at two different positions $(m, n)$.\n\n## Remarks\n\nThe column $n = 0$ consists of the [[Taylor polynomials|0HFSFVMWQB]] of $f$.\nBy a theorem of Padé, the positions where a given rational function occurs form a square block, possibly infinite.\nExample: for $f = e^z$ the table is normal, and $[1/1]_f = (2 + z)/(2 - z)$.\nNon-example of normality: for $f = 1/(1 - z) = \\sum z^k$, one has $[m/n]_f = 1/(1 - z)$ for all $m \\ge 0$ and $n \\ge 1$, since $(1 - z) f - 1 = 0$; so this table is not normal.\nOrientation conventions differ: some authors put $m$ along rows and $n$ along columns, others the reverse.\n",
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