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  "body": "\n## Definition\n\nLet $a \\in \\C$, and let $f(z) = \\sum_{k \\ge 0} c_k (z - a)^k$ be a [[power series|0VP56B4EMX]] with positive [[radius of convergence|0660QX1VPR]].\nFor $z \\in \\C$, let $\\gamma_z \\colon [0, 1] \\to \\C$ be the segment $\\gamma_z(t) = a + t(z - a)$.\nThe *Mittag-Leffler star* of $f$ with respect to $a$ is the set of all $z \\in \\C$ with the following property.\n$f$ has an [[analytic continuation|0M3YQJ81NB]] along the [[path|0JDE56HWQ8]] $\\gamma_z$.\n\n## Remarks\n\nExample: for $f(z) = 1/(1 - z) = \\sum_k z^k$ and $a = 0$, the point $z = i$ lies in the star, because the segment from $0$ to $i$ avoids $1$ and $1/(1-z)$ is holomorphic on $\\C \\setminus \\set{1}$.\nThe star is $\\C \\setminus [1, \\infty)$.\nNon-example: $z = 2$ is not in the star, because the segment from $0$ to $2$ passes through the pole $1$, where no continuation exists.\nThe star is open, it contains the disc of convergence, and with each point $z$ it contains the whole segment from $a$ to $z$.\nFor an entire function the star is all of $\\C$.\n",
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