"zeta function" meaning in English

See zeta function in All languages combined, or Wiktionary

Noun

Forms: zeta functions [plural]
Head templates: {{en-noun}} zeta function (plural zeta functions)
  1. (mathematics) function of the complex variable s that analytically continues the sum of the infinite series ∑ₙ₌₁ ᪲1/(nˢ) that converges when the real part of s is greater than 1. Categories (topical): Functions, Mathematics Translations (function): zeeta-funktio (Finnish), ζ-Funktion [feminine] (German), zeta-fonksiyonu (Turkish)
    Sense id: en-zeta_function-en-noun-AqA2N6Jg Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Finnish translations, Terms with German translations, Terms with Turkish translations Topics: mathematics, sciences Hyponyms: Airy zeta-function, Arakawa–Kaneko zeta-function, arithmetic zeta-function, Artin–Mazur zeta-function, Barnes zeta-function, Beurling zeta-function, Dedekind zeta-function, double zeta-function, Epstein zeta-function, Euler-Riemann zeta-function, Goss zeta-function, Hasse–Weil zeta-function, height zeta-function, Hurwitz zeta-function, Igusa zeta-function, Ihara zeta-function, Lefschetz zeta-function, Lerch zeta-function, L-function, local zeta-function, Matsumoto zeta-function, Minakshisundaram–Pleijel zeta-function, Mordell–Tornheim zeta-function, Motivic zeta-function, multiple zeta-function, p-adic zeta-function, prime zeta-function, Riemann zeta-function, Ruelle zeta-function, Selberg zeta-function, Shimizu L-function, Shintani zeta-function, subgroup zeta-function, Witten zeta-function

Inflected forms

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    {
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      "tags": [
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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        {
          "kind": "other",
          "name": "English entries with incorrect language header",
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        },
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          "parents": [],
          "source": "w"
        },
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          "kind": "topical",
          "langcode": "en",
          "name": "Functions",
          "orig": "en:Functions",
          "parents": [
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            "Calculus",
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        }
      ],
      "glosses": [
        "function of the complex variable s that analytically continues the sum of the infinite series ∑ₙ₌₁ ᪲1/(nˢ) that converges when the real part of s is greater than 1."
      ],
      "hyponyms": [
        {
          "word": "Airy zeta-function"
        },
        {
          "word": "Arakawa–Kaneko zeta-function"
        },
        {
          "word": "arithmetic zeta-function"
        },
        {
          "word": "Artin–Mazur zeta-function"
        },
        {
          "word": "Barnes zeta-function"
        },
        {
          "word": "Beurling zeta-function"
        },
        {
          "word": "Dedekind zeta-function"
        },
        {
          "word": "double zeta-function"
        },
        {
          "word": "Epstein zeta-function"
        },
        {
          "word": "Euler-Riemann zeta-function"
        },
        {
          "word": "Goss zeta-function"
        },
        {
          "word": "Hasse–Weil zeta-function"
        },
        {
          "word": "height zeta-function"
        },
        {
          "word": "Hurwitz zeta-function"
        },
        {
          "word": "Igusa zeta-function"
        },
        {
          "word": "Ihara zeta-function"
        },
        {
          "word": "Lefschetz zeta-function"
        },
        {
          "word": "Lerch zeta-function"
        },
        {
          "word": "L-function"
        },
        {
          "word": "local zeta-function"
        },
        {
          "word": "Matsumoto zeta-function"
        },
        {
          "word": "Minakshisundaram–Pleijel zeta-function"
        },
        {
          "word": "Mordell–Tornheim zeta-function"
        },
        {
          "word": "Motivic zeta-function"
        },
        {
          "word": "multiple zeta-function"
        },
        {
          "word": "p-adic zeta-function"
        },
        {
          "word": "prime zeta-function"
        },
        {
          "word": "Riemann zeta-function"
        },
        {
          "word": "Ruelle zeta-function"
        },
        {
          "word": "Selberg zeta-function"
        },
        {
          "word": "Shimizu L-function"
        },
        {
          "word": "Shintani zeta-function"
        },
        {
          "word": "subgroup zeta-function"
        },
        {
          "word": "Witten zeta-function"
        }
      ],
      "id": "en-zeta_function-en-noun-AqA2N6Jg",
      "links": [
        [
          "mathematics",
          "mathematics"
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        [
          "function",
          "function"
        ],
        [
          "complex variable",
          "complex variable"
        ],
        [
          "infinite series",
          "infinite series"
        ],
        [
          "real part",
          "real part"
        ]
      ],
      "raw_glosses": [
        "(mathematics) function of the complex variable s that analytically continues the sum of the infinite series ∑ₙ₌₁ ᪲1/(nˢ) that converges when the real part of s is greater than 1."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "function",
          "word": "zeeta-funktio"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "function",
          "tags": [
            "feminine"
          ],
          "word": "ζ-Funktion"
        },
        {
          "code": "tr",
          "lang": "Turkish",
          "sense": "function",
          "word": "zeta-fonksiyonu"
        }
      ]
    }
  ],
  "word": "zeta function"
}

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      "tags": [
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      ]
    }
  ],
  "head_templates": [
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      "args": {},
      "expansion": "zeta function (plural zeta functions)",
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      "word": "Airy zeta-function"
    },
    {
      "word": "Arakawa–Kaneko zeta-function"
    },
    {
      "word": "arithmetic zeta-function"
    },
    {
      "word": "Artin–Mazur zeta-function"
    },
    {
      "word": "Barnes zeta-function"
    },
    {
      "word": "Beurling zeta-function"
    },
    {
      "word": "Dedekind zeta-function"
    },
    {
      "word": "double zeta-function"
    },
    {
      "word": "Epstein zeta-function"
    },
    {
      "word": "Euler-Riemann zeta-function"
    },
    {
      "word": "Goss zeta-function"
    },
    {
      "word": "Hasse–Weil zeta-function"
    },
    {
      "word": "height zeta-function"
    },
    {
      "word": "Hurwitz zeta-function"
    },
    {
      "word": "Igusa zeta-function"
    },
    {
      "word": "Ihara zeta-function"
    },
    {
      "word": "Lefschetz zeta-function"
    },
    {
      "word": "Lerch zeta-function"
    },
    {
      "word": "L-function"
    },
    {
      "word": "local zeta-function"
    },
    {
      "word": "Matsumoto zeta-function"
    },
    {
      "word": "Minakshisundaram–Pleijel zeta-function"
    },
    {
      "word": "Mordell–Tornheim zeta-function"
    },
    {
      "word": "Motivic zeta-function"
    },
    {
      "word": "multiple zeta-function"
    },
    {
      "word": "p-adic zeta-function"
    },
    {
      "word": "prime zeta-function"
    },
    {
      "word": "Riemann zeta-function"
    },
    {
      "word": "Ruelle zeta-function"
    },
    {
      "word": "Selberg zeta-function"
    },
    {
      "word": "Shimizu L-function"
    },
    {
      "word": "Shintani zeta-function"
    },
    {
      "word": "subgroup zeta-function"
    },
    {
      "word": "Witten zeta-function"
    }
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  "lang_code": "en",
  "pos": "noun",
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        "Terms with German translations",
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        "function of the complex variable s that analytically continues the sum of the infinite series ∑ₙ₌₁ ᪲1/(nˢ) that converges when the real part of s is greater than 1."
      ],
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        [
          "mathematics",
          "mathematics"
        ],
        [
          "function",
          "function"
        ],
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          "complex variable",
          "complex variable"
        ],
        [
          "infinite series",
          "infinite series"
        ],
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          "real part",
          "real part"
        ]
      ],
      "raw_glosses": [
        "(mathematics) function of the complex variable s that analytically continues the sum of the infinite series ∑ₙ₌₁ ᪲1/(nˢ) that converges when the real part of s is greater than 1."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "function",
      "word": "zeeta-funktio"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "function",
      "tags": [
        "feminine"
      ],
      "word": "ζ-Funktion"
    },
    {
      "code": "tr",
      "lang": "Turkish",
      "sense": "function",
      "word": "zeta-fonksiyonu"
    }
  ],
  "word": "zeta function"
}

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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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