"transcendental function" meaning in English

{
  "forms": [
    {
      "form": "transcendental functions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "transcendental function (plural transcendental functions)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "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": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "An analytic function is transcendental (i.e., is a transcendental function) if and only if its Riemann surface is noncompact.",
          "type": "example"
        }
      ],
      "glosses": [
        "Any function that is algebraically independent of its variable(s); a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials."
      ],
      "id": "en-transcendental_function-en-noun-PFluevxY",
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "algebraically independent",
          "algebraically independent"
        ],
        [
          "variable",
          "variable"
        ],
        [
          "polynomial equation",
          "polynomial equation"
        ],
        [
          "coefficient",
          "coefficient"
        ],
        [
          "polynomial",
          "polynomial"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) Any function that is algebraically independent of its variable(s); a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Complex analysis",
          "orig": "en:Complex analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "41 59",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "38 62",
          "kind": "other",
          "name": "English entries with topic categories using raw markup",
          "parents": [
            "Entries with topic categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "43 57",
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "A meromorphic function on the complex plane that is not a rational function."
      ],
      "id": "en-transcendental_function-en-noun-swo6-Zqd",
      "links": [
        [
          "complex analysis",
          "complex analysis"
        ],
        [
          "meromorphic",
          "meromorphic"
        ],
        [
          "complex plane",
          "complex plane"
        ],
        [
          "rational function",
          "rational function"
        ]
      ],
      "raw_glosses": [
        "(specifically, complex analysis) A meromorphic function on the complex plane that is not a rational function."
      ],
      "tags": [
        "specifically"
      ],
      "topics": [
        "complex-analysis",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "transcendental function"
}

{
  "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"
  ],
  "forms": [
    {
      "form": "transcendental functions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "transcendental function (plural transcendental functions)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English terms with usage examples",
        "en:Functions",
        "en:Mathematical analysis"
      ],
      "examples": [
        {
          "text": "An analytic function is transcendental (i.e., is a transcendental function) if and only if its Riemann surface is noncompact.",
          "type": "example"
        }
      ],
      "glosses": [
        "Any function that is algebraically independent of its variable(s); a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "algebraically independent",
          "algebraically independent"
        ],
        [
          "variable",
          "variable"
        ],
        [
          "polynomial equation",
          "polynomial equation"
        ],
        [
          "coefficient",
          "coefficient"
        ],
        [
          "polynomial",
          "polynomial"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) Any function that is algebraically independent of its variable(s); a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Complex analysis"
      ],
      "glosses": [
        "A meromorphic function on the complex plane that is not a rational function."
      ],
      "links": [
        [
          "complex analysis",
          "complex analysis"
        ],
        [
          "meromorphic",
          "meromorphic"
        ],
        [
          "complex plane",
          "complex plane"
        ],
        [
          "rational function",
          "rational function"
        ]
      ],
      "raw_glosses": [
        "(specifically, complex analysis) A meromorphic function on the complex plane that is not a rational function."
      ],
      "tags": [
        "specifically"
      ],
      "topics": [
        "complex-analysis",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "transcendental function"
}