See infinite series on Wiktionary
Download JSON data for infinite series meaning in All languages combined (3.0kB)
{
"forms": [
{
"form": "infinite series",
"tags": [
"plural"
]
}
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"1": "infinite series"
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"expansion": "infinite series (plural infinite series)",
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"lang": "English",
"lang_code": "en",
"pos": "noun",
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{
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"name": "Infinity",
"orig": "en:Infinity",
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{
"kind": "topical",
"langcode": "en",
"name": "Mathematical analysis",
"orig": "en:Mathematical analysis",
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"examples": [
{
"text": "In 1734, Leonhard Euler solved the Basel problem by summing the infinite series #x5C;textstyle#x5C;frac#x7B;1#x7D;#x7B;1²#x7D;#x2B;#x5C;frac#x7B;1#x7D;#x7B;2²#x7D;#x2B;#x5C;frac#x7B;1#x7D;#x7B;3²#x7D;#x2B;#x5C;cdots#x3D;#x5C;sum#x5F;#x7B;n#x3D;1#x7D;#x7B;#x5C;infty#x7D;#x5C;frac#x7B;1#x7D;#x7B;n²#x7D;#x3D;#x5C;frac#x7B;#x5C;pi²#x7D;#x7B;6#x7D;.",
"type": "example"
}
],
"glosses": [
"Any expression that represents the addition a countably infinite number of ordered summands, often explicitly indexed by the positive or nonnegative integers."
],
"id": "en-infinite_series-en-noun-hOGQx4m3",
"links": [
[
"mathematical analysis",
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[
"countably infinite",
"countably infinite"
],
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"positive",
"positive"
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[
"nonnegative",
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],
[
"integer",
"integer"
]
],
"raw_glosses": [
"(mathematical analysis) Any expression that represents the addition a countably infinite number of ordered summands, often explicitly indexed by the positive or nonnegative integers."
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
],
"translations": [
{
"code": "da",
"lang": "Danish",
"sense": "infinite series",
"word": "uendelig række"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "mugenkyūsū",
"sense": "infinite series",
"word": "無限級数"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "infinite series",
"tags": [
"feminine"
],
"word": "serie infinită"
},
{
"code": "ru",
"lang": "Russian",
"roman": "beskonéčnyj rjad",
"sense": "infinite series",
"tags": [
"masculine"
],
"word": "бесконе́чный ряд"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "infinite series",
"tags": [
"masculine"
],
"word": "beskonačni red"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "infinite series",
"word": "awangganing dalayray"
}
]
}
],
"word": "infinite series"
}
{
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"examples": [
{
"text": "In 1734, Leonhard Euler solved the Basel problem by summing the infinite series #x5C;textstyle#x5C;frac#x7B;1#x7D;#x7B;1²#x7D;#x2B;#x5C;frac#x7B;1#x7D;#x7B;2²#x7D;#x2B;#x5C;frac#x7B;1#x7D;#x7B;3²#x7D;#x2B;#x5C;cdots#x3D;#x5C;sum#x5F;#x7B;n#x3D;1#x7D;#x7B;#x5C;infty#x7D;#x5C;frac#x7B;1#x7D;#x7B;n²#x7D;#x3D;#x5C;frac#x7B;#x5C;pi²#x7D;#x7B;6#x7D;.",
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],
"glosses": [
"Any expression that represents the addition a countably infinite number of ordered summands, often explicitly indexed by the positive or nonnegative integers."
],
"links": [
[
"mathematical analysis",
"mathematical analysis"
],
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"countably infinite",
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],
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"raw_glosses": [
"(mathematical analysis) Any expression that represents the addition a countably infinite number of ordered summands, often explicitly indexed by the positive or nonnegative integers."
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
]
}
],
"translations": [
{
"code": "da",
"lang": "Danish",
"sense": "infinite series",
"word": "uendelig række"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "mugenkyūsū",
"sense": "infinite series",
"word": "無限級数"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "infinite series",
"tags": [
"feminine"
],
"word": "serie infinită"
},
{
"code": "ru",
"lang": "Russian",
"roman": "beskonéčnyj rjad",
"sense": "infinite series",
"tags": [
"masculine"
],
"word": "бесконе́чный ряд"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "infinite series",
"tags": [
"masculine"
],
"word": "beskonačni red"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "infinite series",
"word": "awangganing dalayray"
}
],
"word": "infinite series"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-09 from the enwiktionary dump dated 2024-05-02 using wiktextract (4d5d0bb and edd475d). 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.