{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "072W67KFYK"
    },
    {
      "field": "uses",
      "target": "08RT9GDDPQ"
    },
    {
      "field": "uses",
      "target": "2P0V6X8GZ3"
    },
    {
      "field": "uses",
      "target": "39HWNYW5EF"
    },
    {
      "field": "uses",
      "target": "3N54R6HR05"
    },
    {
      "field": "uses",
      "target": "49JSD49P7X"
    },
    {
      "field": "uses",
      "target": "4WSR1VXJNW"
    },
    {
      "field": "uses",
      "target": "617CH1WRQN"
    },
    {
      "field": "uses",
      "target": "76NQXSGSHS"
    },
    {
      "field": "uses",
      "target": "78GT1VFFPR"
    },
    {
      "field": "uses",
      "target": "7E2ZX7N4VS"
    },
    {
      "field": "uses",
      "target": "BANY9YR82A"
    },
    {
      "field": "uses",
      "target": "H70CF6YBY1"
    },
    {
      "field": "uses",
      "target": "H8RN439272"
    },
    {
      "field": "uses",
      "target": "JZEK70CH3G"
    },
    {
      "field": "uses",
      "target": "KCBFS516DE"
    },
    {
      "field": "uses",
      "target": "M24H4GJPPW"
    },
    {
      "field": "uses",
      "target": "MS8G1FD8FD"
    },
    {
      "field": "uses",
      "target": "N4FACX7QSW"
    },
    {
      "field": "uses",
      "target": "NS852SSQ00"
    },
    {
      "field": "uses",
      "target": "PMYDHW00KF"
    },
    {
      "field": "uses",
      "target": "R587SR9GNV"
    },
    {
      "field": "uses",
      "target": "RC5A5T7YY2"
    },
    {
      "field": "instance_of",
      "target": "0R8JR0ARJ4"
    },
    {
      "field": "about",
      "target": "49JSD49P7X"
    },
    {
      "field": "about",
      "target": "BANY9YR82A"
    }
  ],
  "body": "\n## Summary\n\nA formal power series is an infinite sum $\\sum a_n X^n$ treated as an algebraic object, without any convergence condition. Formal power series form a ring that is the natural home of generating functions. The node [[formal power series|072W67KFYK]] gives the precise definition.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "inventory": [
      "8BY93JNSJY"
    ],
    "kind": "concept",
    "msc": [
      "13F25"
    ],
    "name": "Formal power series",
    "same_as": {
      "wikidata": "Q1003025",
      "wikipedia": "Formal power series"
    },
    "sources": [
      {
        "locator": "Definition of the formal power series ring",
        "url": "https://en.wikipedia.org/wiki/Formal_power_series"
      }
    ],
    "tag": "033WGN00BF"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/033WGN00BF/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/033WGN00BF.md",
  "msc": [
    "13F25"
  ],
  "name": "Formal power series",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/033/033WGN00BF.md",
  "status": null,
  "tag": "033WGN00BF",
  "uri": "m2://033WGN00BF",
  "url": "https://tamnd.github.io/math2/wiki/formal-power-series/",
  "writing": {
    "tag": "033WGN00BF",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 1,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}