"smooth function" meaning in English

{
  "etymology_text": "smooth + function",
  "forms": [
    {
      "form": "smooth functions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "smooth function (plural smooth functions)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with topic categories using raw markup",
          "parents": [
            "Entries with topic categories using raw markup",
            "Entry maintenance"
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          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
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          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Functions",
          "orig": "en:Functions",
          "parents": [
            "Algebra",
            "Calculus",
            "Geometry",
            "Mathematical analysis",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Shapes",
          "orig": "en:Shapes",
          "parents": [
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2003, Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, page 419",
          "text": "Any ANALYTIC FUNCTION is smooth. But a smooth function is not necessarily analytic.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "a function that has derivatives of all finite orders everywhere in its domain."
      ],
      "id": "en-smooth_function-en-noun-IipSbcIp",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "derivative",
          "derivative"
        ],
        [
          "finite",
          "finite"
        ],
        [
          "order",
          "order"
        ],
        [
          "domain",
          "domain"
        ]
      ],
      "raw_glosses": [
        "(mathematics) a function that has derivatives of all finite orders everywhere in its domain."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "sv",
          "lang": "Swedish",
          "sense": "function that has derivatives of all finite orders everywhere in its domain",
          "tags": [
            "common-gender"
          ],
          "word": "slät funktion"
        },
        {
          "code": "sv",
          "lang": "Swedish",
          "sense": "function that has derivatives of all finite orders everywhere in its domain",
          "tags": [
            "common-gender"
          ],
          "word": "glatt funktion"
        }
      ],
      "wikipedia": [
        "smooth function"
      ]
    }
  ],
  "word": "smooth function"
}

{
  "etymology_text": "smooth + function",
  "forms": [
    {
      "form": "smooth functions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "smooth function (plural smooth functions)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English entries with topic categories using raw markup",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys",
        "English terms with quotations",
        "en:Functions",
        "en:Mathematics",
        "en:Shapes"
      ],
      "examples": [
        {
          "ref": "2003, Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, page 419",
          "text": "Any ANALYTIC FUNCTION is smooth. But a smooth function is not necessarily analytic.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "a function that has derivatives of all finite orders everywhere in its domain."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "derivative",
          "derivative"
        ],
        [
          "finite",
          "finite"
        ],
        [
          "order",
          "order"
        ],
        [
          "domain",
          "domain"
        ]
      ],
      "raw_glosses": [
        "(mathematics) a function that has derivatives of all finite orders everywhere in its domain."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "smooth function"
      ]
    }
  ],
  "translations": [
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "function that has derivatives of all finite orders everywhere in its domain",
      "tags": [
        "common-gender"
      ],
      "word": "slät funktion"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "function that has derivatives of all finite orders everywhere in its domain",
      "tags": [
        "common-gender"
      ],
      "word": "glatt funktion"
    }
  ],
  "word": "smooth function"
}