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  "body": "\n## Summary\n\nWiman–Valiron theory studies a transcendental [[entire function|0419794R0T]] through the largest term of its [[Taylor series|0225QPWRRE]] on each circle $\\abs{z} = r$.\nThe index of this maximal term, the central index $\\nu(r)$, grows to infinity with $r$.\nNear points where $\\abs{f}$ attains its maximum on the circle, $f$ behaves like the single monomial $a_{\\nu(r)} z^{\\nu(r)}$, outside a small exceptional set of radii.\nA main application is to the growth of entire solutions of linear differential equations with polynomial coefficients.\n\n## Explanations\n\n### L1 human\n\nAn entire function is an infinite sum of terms $a_n z^n$.\nOn a large circle, one term is usually much bigger than the others, and its index is the central index.\nNear the point where the function is largest on the circle, the function looks like this one term.\nIn particular, each derivative multiplies the function by about $\\nu(r)/z$, as for a monomial.\nFor $e^z$ the central index on the circle of radius $r$ is about $r$, and indeed $(e^z)' = e^z \\approx (r/z) e^z$ near $z = r$.\n",
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