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@7shi 7shi/Bessel.ipynb
Last active Sep 24, 2018

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Reverse Bessel Polynomial
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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/plain": [
"<IPython.core.display.Math object>"
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"output_type": "display_data"
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{
"data": {
"text/latex": [
"$$\\theta_{1}(s) = s + 1$$"
],
"text/plain": [
"<IPython.core.display.Math object>"
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"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/latex": [
"$$\\theta_{2}(s) = s^{2} + 3 s + 3$$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/latex": [
"$$\\theta_{3}(s) = s^{3} + 6 s^{2} + 15 s + 15$$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/latex": [
"$$\\theta_{4}(s) = s^{4} + 10 s^{3} + 45 s^{2} + 105 s + 105$$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$$\\theta_{5}(s) = s^{5} + 15 s^{4} + 105 s^{3} + 420 s^{2} + 945 s + 945$$"
],
"text/plain": [
"<IPython.core.display.Math object>"
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"output_type": "display_data"
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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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"nbformat": 4,
"nbformat_minor": 2
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