Reverse Bessel Polynomial

Bessel.ipynb

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    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sympy as sb\n",
    "from IPython.display import display, Math\n",
    "sb.init_printing()\n",
    "\n",
    "plt.rcParams[\"font.size\"] = 12\n",
    "\n",
    "fac =  sb.factorial\n",
    "s   = sb.Symbol('s')\n",
    "ω   = sb.Symbol('ω',real=True)\n",
    "\n",
    "N = 6"
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      "text/latex": [
       "$$\\theta_{0}(s) = 1$$"
      ],
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      "text/latex": [
       "$$\\theta_{1}(s) = s + 1$$"
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     "data": {
      "text/latex": [
       "$$\\theta_{2}(s) = s^{2} + 3 s + 3$$"
      ],
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     "data": {
      "text/latex": [
       "$$\\theta_{3}(s) = s^{3} + 6 s^{2} + 15 s + 15$$"
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     "data": {
      "text/latex": [
       "$$\\theta_{4}(s) = s^{4} + 10 s^{3} + 45 s^{2} + 105 s + 105$$"
      ],
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     "data": {
      "text/latex": [
       "$$\\theta_{5}(s) = s^{5} + 15 s^{4} + 105 s^{3} + 420 s^{2} + 945 s + 945$$"
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   "source": [
    "# Reverse Bessel Polynomial\n",
    "def θn(n):\n",
    "    y = 0\n",
    "    for k in range(n+1):\n",
    "        y += fac(n+k)/(fac(n-k)*fac(k)) * (s**(n-k)/2**k)\n",
    "    return y\n",
    "\n",
    "θ = []\n",
    "for n in range(N):\n",
    "    θ.append(θn(n))\n",
    "    display(Math(r\"\\theta_{%d}(s) = %s\" % (n, sb.latex(θn(n)))))"
   ]
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References

• https://twitter.com/ceptree/status/1044169194105843713
• https://gist.github.com/ceptreee/8144758ff3d71759018cc18c0fe63c8d
• Is it possible to show print output as LaTeX in jupyter notebook?