{
  "aliases": [
    "multiplicity-of-a-pole"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "0YK27TJ4WF"
    }
  ],
  "body": "\n## Summary\n\nThe order of a pole $c$ of $f$ is the integer $m \\ge 1$ with the following property. The function $(z - c)^m f(z)$ extends to a holomorphic function near $c$ that is not $0$ at $c$, see the [[definition|0YK27TJ4WF]].\n",
  "commit": "545acf83a9b75c8ddc375ef8b23d2ae101a4d7e4",
  "front": {
    "aliases": [
      "multiplicity-of-a-pole"
    ],
    "kind": "concept",
    "msc": [
      "30D30"
    ],
    "name": "Order of a pole",
    "sources": [
      {
        "locator": "Definitions",
        "url": "https://en.wikipedia.org/wiki/Zeros_and_poles"
      }
    ],
    "tag": "073MWACF1K"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/073MWACF1K/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/073MWACF1K.md",
  "msc": [
    "30D30"
  ],
  "name": "Order of a pole",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/073/073MWACF1K.md",
  "status": null,
  "tag": "073MWACF1K",
  "uri": "m2://073MWACF1K",
  "url": "https://math2.tamnd.com/wiki/order-of-a-pole/",
  "writing": {
    "tag": "073MWACF1K",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}