{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots, ComplexPhasePortrait, ApproxFun\n",
    "gr();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\def\\E{{\\rm e}}\n",
    "$$\n",
    "\n",
    "# M3M6: Methods of Mathematical Physics\n",
    "\n",
    "Dr. Sheehan Olver\n",
    "<br>\n",
    "s.olver@imperial.ac.uk\n",
    "\n",
    "<br>\n",
    "Website: Blackboard\n",
    "\n",
    "\n",
    "\n",
    "# Lecture 6: Analytic functions at infinity\n",
    "\n",
    "\n",
    "This lecture we cover\n",
    "\n",
    "1. Riemann sphere and analyticity at infinity\n",
    "     - Cauchy's integral formula exterior to a contour\n",
    "     - Exterior Residue theorem \n",
    "2. Reperesenting functions by their behaviour near singularities\n",
    "     - Application: Partial fraction expansion\n",
    "\n",
    "\n",
    "\n",
    "## Riemann sphere and analyticity at infinity\n",
    "\n",
    "**Definition (Riemann sphere)** The _Riemann sphere_ is the compactification of ${\\mathbb C}$:\n",
    "$$\n",
    "    \\bar {\\mathbb C} = {\\mathbb C} \\cup \\{\\infty\\}\n",
    "$$\n",
    "\n",
    "Without delving on the details, we can define an open set $D \\subset \\bar{\\mathbb C}$ on the Riemann sphere, where $\\infty \\in D$ implies that there exists an $R$ such that $\\{ z : |z| > R\\} \\subset D$.\n",
    "\n",
    "\n",
    "**Definition (Analytic at infinity)** A function $f(z)$ defined on an open set $D \\subset \\bar {\\mathbb C}$ such that $\\infty \\in D$ is _analytic at ∞_ if $f(z^{-1})$ is analytic at zero.\n",
    "\n",
    "**Proposition (Taylor series at infinity)** If $f$ is analytic at infinity, then there exists an $R$ such that for all $|z| > R$ we have\n",
    "$$\n",
    "f(z) = \\sum_{k=-\\infty}^0 f_k z^k \n",
    "$$\n",
    "The coefficients $f_k$ are defined by\n",
    "$$\n",
    "f_k = {1 \\over 2 \\pi i} \\oint_\\gamma {f(z) \\over z^{k+1}} dz\n",
    "$$\n",
    "where $\\gamma$ is any simple closed positively oriented contour such that $f$ is analytic outside of.\n",
    "\n",
    "_Demonstration_ $f(z) = \\E^{1/z}$ is not analytic at zero, but is analytic at infinity because $f(1/z) = \\E^z$ is analytic at zero:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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       "\" transform=\"translate(149, 47)\"/>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = z -> exp(1/z)\n",
    "phaseplot(-6..6, -6..6, f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We therefore have a convergence \"Taylor\" series in inverse powers of $z$:\n",
    "$$\n",
    "\\E^{1/z} = 1 + {1 \\over z} + {1 \\over 2 z^2} + {1 \\over 3! z^3} + \\cdots\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.220446049250313e-16 - 5.551115123125783e-17im"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = 2.0+2im\n",
    "sum([z^k/factorial(-1.0k) for k=-100:0]) - exp(1/z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These coefficients can be calculated as integrals:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.4867941867133823e-16 + 1.13303848301229e-16im"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k=-5;\n",
    "sum(Fun(z -> f(z)/z^(k+1), Circle()))/(2π*im) - 1/factorial(-1.0k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Theorem (Cauchy's integral theorem near infinity)** Suppose $f$ is analytic outside and on a positively oriented, simple, closed contour $\\gamma$, and \n",
    "$$f(\\infty) = 0.$$ \n",
    "Then we have\n",
    "$$\n",
    "f(z) = -{1 \\over 2 \\pi i} \\oint {f(\\zeta) \\over \\zeta - z} d \\zeta\n",
    "$$\n",
    "\n",
    "*Example* The function $f(z) = \\E^{1/z} - 1$ vanishes at $\\infty$ and so can thence be recovered as a Cauchy integral:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.220446049250313e-16 + 5.551115123125783e-17im"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = z -> exp(1/z) - 1\n",
    "\n",
    "ζ = Fun(Circle())\n",
    "-sum(f.(ζ)/(ζ-z))/(2π*im) - f(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The decay at infinity is required:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.9999999999999997 + 5.551115123125783e-17im"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = z -> exp(1/z) \n",
    "\n",
    "ζ = Fun(Circle())\n",
    "-sum(f.(ζ)/(ζ-z))/(2π*im) - f(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Exterior Residue theorem\n",
    "\n",
    "**Definition (Residue at infinity)** Suppose $f$ is analytic in the annulus $A_{R\\infty} = \\{z : R < |z| < \\infty \\}$. Then the residue at infinity is\n",
    "$$\n",
    "{\\underset{z = \\infty}{\\rm Res}} \\, f(z) = -f_{-1}\n",
    "$$\n",
    "where $f_{-1}$ is (again) the Laurent coefficient for any circle in $A_{R\\infty}$.\n",
    "\n",
    "**Theorem (Exterier Residue Theorem)** Let $f$ be holomprohic outside and on a simple closed, positively oriented contour $\\gamma$ except at isolated points $z_1, \\ldots, z_r$ outside $\\gamma$. Then\n",
    "\n",
    "$$\\oint_\\gamma f(z) dz = -2 \\pi i \\sum_{j=1}^r {\\underset{z = z_j}{\\rm Res}}\\, f(z)$$ \n",
    "\n",
    "\n",
    "Let's return to our simple examples from before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = z -> 1/(z*(z+2))\n",
    "phaseplot(-3..3, -3..3, f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because it is analytic outside a circle of radius 3 and decays like $O(z^{-2})$, its residue at infinity is zero:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.191214874231192e-18 - 8.870531755418961e-17im"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(Fun(f, Circle(3.0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's another example with singularities at $0$ and $-2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "Z7dbbU/3hv04fY2dnn8AoF8cSIQIkXV2xVpEdDvru2q763nZuT/WHBt323trpZiL7irFjqyIy9m5\n",
       "nsoq1alyTEflaJLKc5t1i9zoFG+yqradzteVTns4y/wd1Hk/rpy2ng/jVP7eDQAAAAAAAADABRc+\n",
       "AAAAAAAAAACaCUe6RFRui/nJzpsx4k1q63RrqtNcu+lW227z/anT10c9zhzA/+kWPxHRKbLiDTrt\n",
       "R7cIkU46nYMx6kSGOH/r7Px92O15+JesFumrVIq1WBGJsnMup62n0lxWqRLLs0qn2o/xvtgU/mNF\n",
       "bbudr5mImnusJ2ZTxEurz/sAAAAAAAAAAIzx/wDE9chZVlW/JQAAAABJRU5ErkJggg==\n",
       "\" transform=\"translate(149, 47)\"/>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = z -> 1/z + 1/(z+2)\n",
    "phaseplot(-3..3, -3..3, f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This has a residue at infinity:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.7038443268502702e-15 + 12.566370614359174im, 0.0 + 12.566370614359172im)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f₋₁ = 2\n",
    "res∞ = -f₋₁\n",
    "sum(Fun(f, Circle(3.0))), -2π*im*res∞"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On a smaller circle of radius 1 we pick up another term:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.032906916559743e-15 + 6.283185307179586im, 0.0 + 6.283185307179586im)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res∞ = -2\n",
    "res₋₂ = 1\n",
    "sum(Fun(f, Circle(1.0))), -2π*im*(res∞ + res₋₂)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a more complicated example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "400×400 Array{RGB{Float64},2} with eltype RGB{Float64}:\n",
       " RGB{Float64}(0.217028,1.0,0.0)  …  RGB{Float64}(0.577629,0.0,1.0)\n",
       " RGB{Float64}(0.227045,1.0,0.0)     RGB{Float64}(0.577629,0.0,1.0)\n",
       " RGB{Float64}(0.227045,1.0,0.0)     RGB{Float64}(0.587646,0.0,1.0)\n",
       " RGB{Float64}(0.227045,1.0,0.0)     RGB{Float64}(0.587646,0.0,1.0)\n",
       " RGB{Float64}(0.237062,1.0,0.0)     RGB{Float64}(0.597663,0.0,1.0)\n",
       " RGB{Float64}(0.237062,1.0,0.0)  …  RGB{Float64}(0.597663,0.0,1.0)\n",
       " RGB{Float64}(0.237062,1.0,0.0)     RGB{Float64}(0.607679,0.0,1.0)\n",
       " RGB{Float64}(0.247078,1.0,0.0)     RGB{Float64}(0.607679,0.0,1.0)\n",
       " RGB{Float64}(0.247078,1.0,0.0)     RGB{Float64}(0.617696,0.0,1.0)\n",
       " RGB{Float64}(0.257095,1.0,0.0)     RGB{Float64}(0.617696,0.0,1.0)\n",
       " RGB{Float64}(0.257095,1.0,0.0)  …  RGB{Float64}(0.627713,0.0,1.0)\n",
       " RGB{Float64}(0.257095,1.0,0.0)     RGB{Float64}(0.627713,0.0,1.0)\n",
       " RGB{Float64}(0.267112,1.0,0.0)     RGB{Float64}(0.63773,0.0,1.0) \n",
       " ⋮                               ⋱                                \n",
       " RGB{Float64}(0.257095,0.0,1.0)     RGB{Float64}(0.627713,1.0,0.0)\n",
       " RGB{Float64}(0.257095,0.0,1.0)     RGB{Float64}(0.627713,1.0,0.0)\n",
       " RGB{Float64}(0.257095,0.0,1.0)  …  RGB{Float64}(0.617696,1.0,0.0)\n",
       " RGB{Float64}(0.247078,0.0,1.0)     RGB{Float64}(0.617696,1.0,0.0)\n",
       " RGB{Float64}(0.247078,0.0,1.0)     RGB{Float64}(0.607679,1.0,0.0)\n",
       " RGB{Float64}(0.237062,0.0,1.0)     RGB{Float64}(0.607679,1.0,0.0)\n",
       " RGB{Float64}(0.237062,0.0,1.0)     RGB{Float64}(0.597663,1.0,0.0)\n",
       " RGB{Float64}(0.237062,0.0,1.0)  …  RGB{Float64}(0.597663,1.0,0.0)\n",
       " RGB{Float64}(0.227045,0.0,1.0)     RGB{Float64}(0.587646,1.0,0.0)\n",
       " RGB{Float64}(0.227045,0.0,1.0)     RGB{Float64}(0.587646,1.0,0.0)\n",
       " RGB{Float64}(0.227045,0.0,1.0)     RGB{Float64}(0.577629,1.0,0.0)\n",
       " RGB{Float64}(0.217028,0.0,1.0)     RGB{Float64}(0.577629,1.0,0.0)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = z -> exp(1/z)/(z*(z+2))\n",
    "portrait(-3..3, -3..3, f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example has an essential singularity at zero so the classical Residue theorem is not much use, but we can use the residue theorem at infinity:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2241051404579888e-18 - 1.191336987305697e-16im"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(Fun(f, Circle(3.0)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-4.3477951067425517e-16 + 1.9054722647301798im, 0.0 + 1.9054722647301798im)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(Fun(f, Circle(1.0))), -2π*im * exp(-1/2)/(-2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Representing analytic functions by their behaviour near singularities\n",
    "\n",
    "A _key_ theme in complex analysis is representing functions by their behaviour near singularities.  A rather simple example of this is a side-effect of Cauchy's integral representation:\n",
    "\n",
    "**Corollary (Cauchy's integral representation around holes)** Let $D \\subset {\\mathbb C}$ be a domain with $g$ holes (i.e., genus $g$). Suppose $f$ is holmorphic in and on the boundary of $D$.  Given $g$ simple closed negatively oriented contours  surrounding the holes $\\gamma_1, \\ldots, \\gamma_g$ and a simple closed positively oriented contour $\\gamma_{0}$ surrounding the outer boundary of $D$, we have\n",
    "$$\n",
    "f(z) = {1 \\over 2 \\pi i} \\sum_{k=0}^{g} \\oint_{\\gamma_k} {f(\\zeta) \\over \\zeta - z} d \\zeta\n",
    "$$\n",
    "\n",
    "Here are two examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<?xml version=\"1.0\" encoding=\"utf-8\"?>\n",
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       "  <clipPath id=\"clip6700\">\n",
       "    <rect x=\"0\" y=\"0\" width=\"2000\" height=\"2000\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
       "<defs>\n",
       "  <clipPath id=\"clip6701\">\n",
       "    <rect x=\"0\" y=\"0\" width=\"2400\" height=\"1600\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
       "<polygon clip-path=\"url(#clip6701)\" points=\"\n",
       "0,1600 2400,1600 2400,0 0,0 \n",
       "  \" fill=\"#ffffff\" fill-opacity=\"1\"/>\n",
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       "  <clipPath id=\"clip6702\">\n",
       "    <rect x=\"480\" y=\"0\" width=\"1681\" height=\"1600\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
       "<polygon clip-path=\"url(#clip6701)\" points=\"\n",
       "149.361,1503.47 2321.26,1503.47 2321.26,47.2441 149.361,47.2441 \n",
       "  \" fill=\"#ffffff\" fill-opacity=\"1\"/>\n",
       "<defs>\n",
       "  <clipPath id=\"clip6703\">\n",
       "    <rect x=\"149\" y=\"47\" width=\"2173\" height=\"1457\"/>\n",
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      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = z -> (exp(1/z) + exp(z))/(z*(z+2))\n",
    "Γ = Circle(0.0, 4.0) ∪ Circle(0.0,0.5,false) ∪ Circle(-2.0,0.1,false)\n",
    "phaseplot(-5..5, -5..5, f)\n",
    "plot!(Γ; color=:black, label=:contour, arrow=true, linewidth=1.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8671607060038516 + 0.10261889457156087im"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ζ = Fun(Γ)\n",
    "z = 2.0+1.0im\n",
    "sum(f.(ζ)/(ζ - z))/(2π*im)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8671607060038514 + 0.10261889457156062im"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Application: Partial fraction expansion\n",
    "\n",
    "Suppose we have a rational function \n",
    "$$\n",
    "r(z) = {p(z) \\over q(z)}\n",
    "$$\n",
    "where $p,q$ are both polynomials. This is analytic everywhere apart for the roots of $q$, which we enumerate $\\lambda_1,\\ldots,\\lambda_g$.   If we draw negatively oriented circles around each root, the previous result applies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Complex{Float64},1}:\n",
       "  0.6574583015092604 + 0.8969475017786706im\n",
       "  0.6574583015092604 - 0.8969475017786706im\n",
       " -0.6950370227626129 + 0.0im               \n",
       " -1.5131182364477396 + 0.0im               "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 7\n",
    "m = 5\n",
    "p = Fun(Taylor(), randn(n))\n",
    "q = Fun(Taylor(), randn(m))\n",
    "λ = complexroots(q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Γ = Circle(0.0, 5.0)\n",
    "for λ in λ\n",
    "    Γ = Γ ∪ Circle(λ, 0.1, false)\n",
    "end\n",
    "r = z -> extrapolate(p,z)/extrapolate(q,z)\n",
    "\n",
    "phaseplot(-5..5, -5..5, r)\n",
    "plot!(Γ; color=:black, label=:contour)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.6653345369377348e-16 + 2.6645352591003757e-15im"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ζ = Fun(Γ)\n",
    "z = 2.0+2.0im\n",
    "sum(r.(ζ)/(ζ - z))/(2π*im) - r(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But now we can use the residue theorem to simplify the integrals! Note the following:\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "For example,  near the $j$th root we have the Laurent series\n",
    "$$\n",
    "r(z) = r_{-N_j}^j (z-\\lambda_j)^{-N_j}  + \\cdots + r_{-1}^j (z-\\lambda_j)^{-1} + r_0 + r_1 (z-\\lambda_j) + \\cdots\n",
    "$$\n",
    "where $N_j$ is the order of the zero of $q(z)$ at $\\lambda_j$.\n",
    "\n",
    "Then it follows that\n",
    "$${1 \\over 2 \\pi i} \\oint_{\\gamma_j} {r(\\zeta) \\over z - \\zeta} d\\zeta = r_{-N_j}^j (z-\\lambda_j)^{-N}  + \\cdots + r_{-1}^j (z-\\lambda_j)^{-1}$$\n",
    "for $z$ outside the contour $\\gamma_j$.\n",
    "\n",
    "Similarly, for the contour around infinity $\\gamma_0$, if we have the Laurent series\n",
    "$$\n",
    "r(z) = \\cdots + r_{-1}^0 z^{-1} + r_0^0  + r_1^0 z + \\dots + r_{N_0}^0 z^{N_0}\n",
    "$$\n",
    "where $N_0$ is the degree of $p(z)$ divided by the degree of $q(z)$. \n",
    "Then we have\n",
    "$${1 \\over 2 \\pi i} \\oint_{\\gamma_{g+1}} {r(\\zeta) \\over z - \\zeta} d\\zeta = r_0^0 + r_1^0 z + \\cdots +  r_{N_0}^0 z^{N_0}.$$\n",
    "\n",
    "Thus we have the expansion summing over the behaviour near each singularity that holds for all $z$:\n",
    "\n",
    "$$\n",
    "r(z) = \\sum_{k=0}^{N_0} r_k^0 z^k  +  \\sum_{j=1}^d \\sum_{k = -N_j}^{-1} r_k^j (z - \\lambda_j)^k\n",
    "$$\n",
    "\n",
    "*Example* When we only have simple poles and no polynomial growth at $\\infty$, this has a simple form in terms of residues:\n",
    "\n",
    "$$\n",
    "r(z) = r(\\infty)  +  \\sum_{j=1}^d    (z - \\lambda_j)^{-1} \\underset{z = \\lambda_j}{\\rm Res}\\, r(z)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 5\n",
    "m = 5\n",
    "p = Fun(Taylor(), randn(n))\n",
    "q = Fun(Taylor(), randn(m))\n",
    "λ = complexroots(q)\n",
    "\n",
    "r = z -> extrapolate(p,z)/extrapolate(q,z)\n",
    "\n",
    "phaseplot(-7..7, -7..7, r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "#21 (generic function with 1 method)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = extrapolate.(p,λ)./extrapolate.(q',λ)\n",
    "r∞ = p.coefficients[n]/q.coefficients[m]\n",
    "\n",
    "r̃ = z -> r∞ + sum(res.*(z .- λ).^(-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1102230246251565e-16 - 3.3306690738754696e-16im"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = 0.1+0.2im\n",
    "r(z) - r̃(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
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       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phaseplot(-7..7, -7..7, r̃)"
   ]
  }
 ],
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