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        "value": "The Laguerre polynomials :math:`L_n` are the special case\n:math:`\\alpha = 0` of the generalized Laguerre polynomials\n:math:`L_n^{(\\alpha)}`.\nLet's verify it on the interval :math:`[-1, 1]`:\n\n"
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        "value": "import numpy as np\nfrom scipy.special import genlaguerre\nfrom scipy.special import laguerre\nx = np.arange(-1.0, 1.0, 0.01)\nnp.allclose(genlaguerre(3, 0)(x), laguerre(3)(x))\n",
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        "value": "\nThe polynomials :math:`L_n` also satisfy the recurrence relation:\n\n.. math::\n    (n + 1)L_{n+1}(x) = (2n +1 -x)L_n(x) - nL_{n-1}(x)\n\nThis can be easily checked on :math:`[0, 1]` for :math:`n = 3`:\n\n"
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        "value": "x = np.arange(0.0, 1.0, 0.01)\nnp.allclose(4 * laguerre(4)(x),\n            (7 - x) * laguerre(3)(x) - 3 * laguerre(2)(x))\n",
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        "value": "\nThis is the plot of the first few Laguerre polynomials :math:`L_n`:\n\n"
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        "value": "import matplotlib.pyplot as plt\nx = np.arange(-1.0, 5.0, 0.01)\nfig, ax = plt.subplots()\n",
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      {
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        "value": "ax.set_ylim(-5.0, 5.0)\nax.set_title(r'Laguerre polynomials $L_n$')\nfor n in np.arange(0, 5):\n    ax.plot(x, laguerre(n)(x), label=rf'$L_{n}$')\nplt.legend(loc='best')\n",
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  "references": [
    ".. [AS] Milton Abramowitz and Irene A. Stegun, eds.",
    "    Handbook of Mathematical Functions with Formulas,",
    "    Graphs, and Mathematical Tables. New York: Dover, 1972."
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