updated tutorial

Author: ranocha

notebooks/Tutorial.ipynb

@@ -117,6 +117,36 @@
     "fig"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Gegenbauer Polynomials\n",
+    "\n",
+    "Gegenbauer poylnomials $C_p^{(\\alpha)}$ are evaluated as `gegenbauer(x, p, α)` using the three term recursion formula."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "using Revise\n",
+    "using PolynomialBases\n",
+    "using LaTeXStrings, Plots; pyplot()\n",
+    "\n",
+    "α = 0.5\n",
+    "x = linspace(-1, 1, 10^3)\n",
+    "fig = plot(xguide=L\"x\")\n",
+    "for p in 0:5\n",
+    "    plot!(fig, x, gegenbauer.(x, p, α), label=\"\\$ C_$p^{($α)} \\$\")\n",
+    "end\n",
+    "fig"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -148,6 +178,35 @@
     "fig"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Hermite Polynomials\n",
+    "\n",
+    "Hermite poylnomials $H_p$ are evaluated as `hermite(x, p)` using the three term recursion formula."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "using Revise\n",
+    "using PolynomialBases\n",
+    "using LaTeXStrings, Plots; pyplot()\n",
+    "\n",
+    "x = linspace(-2, 2, 10^3)\n",
+    "fig = plot(xguide=L\"x\")\n",
+    "for p in 0:4\n",
+    "    plot!(fig, x, hermite.(x, p), label=\"\\$ H_$p \\$\")\n",
+    "end\n",
+    "fig"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -266,6 +325,10 @@
    "mimetype": "application/julia",
    "name": "julia",
    "version": "0.6.1"
+  },
+  "widgets": {
+   "state": {},
+   "version": "1.1.2"
   }
  },
  "nbformat": 4,