"Barnes integral" meaning in English

{
  "etymology_text": "They were introduced by Ernest William Barnes.",
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    {
      "form": "Barnes integrals",
      "tags": [
        "plural"
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  "lang_code": "en",
  "pos": "noun",
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          "name": "Functions",
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      "glosses": [
        "A contour integral involving a product of gamma functions, closely related to generalized hypergeometric series."
      ],
      "id": "en-Barnes_integral-en-noun-ML~tZHWg",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "contour integral",
          "contour integral"
        ],
        [
          "product",
          "product"
        ],
        [
          "gamma function",
          "gamma function"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A contour integral involving a product of gamma functions, closely related to generalized hypergeometric series."
      ],
      "synonyms": [
        {
          "word": "Mellin-Barnes integral"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Ernest William Barnes"
      ]
    }
  ],
  "word": "Barnes integral"
}

{
  "etymology_text": "They were introduced by Ernest William Barnes.",
  "forms": [
    {
      "form": "Barnes integrals",
      "tags": [
        "plural"
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      "glosses": [
        "A contour integral involving a product of gamma functions, closely related to generalized hypergeometric series."
      ],
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        [
          "mathematics",
          "mathematics"
        ],
        [
          "contour integral",
          "contour integral"
        ],
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          "product",
          "product"
        ],
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          "gamma function",
          "gamma function"
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      "raw_glosses": [
        "(mathematics) A contour integral involving a product of gamma functions, closely related to generalized hypergeometric series."
      ],
      "synonyms": [
        {
          "word": "Mellin-Barnes integral"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Ernest William Barnes"
      ]
    }
  ],
  "word": "Barnes integral"
}