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        "value": "The Jacobi polynomials satisfy the recurrence relation:\n\n.. math::\n    P_n^{(\\alpha, \\beta-1)}(x) - P_n^{(\\alpha-1, \\beta)}(x)\n      = P_{n-1}^{(\\alpha, \\beta)}(x)\n\nThis can be verified, for example, for :math:`\\alpha = \\beta = 2`\nand :math:`n = 1` over the interval :math:`[-1, 1]`:\n\n"
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        "value": "import numpy as np\nfrom scipy.special import jacobi\nx = np.arange(-1.0, 1.0, 0.01)\nnp.allclose(jacobi(0, 2, 2)(x),\n            jacobi(1, 2, 1)(x) - jacobi(1, 1, 2)(x))\n",
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        "value": "\nPlot of the Jacobi polynomial :math:`P_5^{(\\alpha, -0.5)}` for\ndifferent values of :math:`\\alpha`:\n\n"
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      {
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        "value": "ax.set_ylim(-2.0, 2.0)\nax.set_title(r'Jacobi polynomials $P_5^{(\\alpha, -0.5)}$')\nfor alpha in np.arange(0, 4, 1):\n    ax.plot(x, jacobi(5, alpha, -0.5)(x), label=rf'$\\alpha={alpha}$')\nplt.legend(loc='best')\n",
        "execution_status": "failure"
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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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