See semifactorial on Wiktionary
Download JSON data for semifactorial meaning in All languages combined (3.6kB)
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "semi-",
"3": "factorial"
},
"expansion": "semi- + factorial",
"name": "compound"
}
],
"etymology_text": "semi- + factorial",
"forms": [
{
"form": "semifactorials",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "semifactorial (plural semifactorials)",
"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": "topical",
"langcode": "en",
"name": "Combinatorics",
"orig": "en:Combinatorics",
"parents": [
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"Sciences",
"All topics",
"Fundamental"
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{
"kind": "topical",
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"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
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"All topics",
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],
"source": "w"
}
],
"examples": [
{
"ref": "1942 February, Giulio Racah, “Theory of Complex Spectra. I”, in Physical Review, volume 61, numbers 3–4, →DOI, page 188",
"text": "With the symbol n#x21;#x21; we indicate the semifactorial of n, that is the product 1.3.5#x5C;dotsn if n is odd, and the product 2.4.6#x5C;dotsn if n is even.",
"type": "quotation"
},
{
"ref": "1994 January, Alan Edelman, Eric Kostlan, Michael Shub, “How many eigenvalues of a random matrix are real?”, in Journal of the American Mathematical Society, volume 7, number 1, →DOI, pages 250–251",
"text": "In the formulas above we use the Euler beta function, a Jacobi polynomial evaluated at three, and also the familiar double factorial (also known as the semifactorial) notation defined by n#x21;#x21;#x3D;#x5C;begin#x7B;cases#x7D;#x5C;displaystyle 1#x5C;times 3#x5C;times 5#x5C;times#x5C;dots#x5C;timesn#x26;#x5C;text#x7B;if#x7D;n#x5C;text#x7B;isodd#x7D;,#x5C;#x5C;#x5B;5pt#x5D;#x5C;displaystyle 2#x5C;times 4#x5C;times 6#x5C;times#x5C;dots#x5C;timesn#x26;#x5C;text#x7B;if#x7D;n#x5C;text#x7B;iseven#x7D;.#x5C;end#x7B;cases#x7D;By convention, 0#x21;#x21;#x3D;(-1)#x21;#x21;#x3D;1.",
"type": "quotation"
},
{
"ref": "2009, Keith B. Oldham, Jan C. Myland, Jerome Spanier, An Atlas of Functions, 2nd edition, Springer, →DOI, page 25",
"text": "The double factorial or semifactorial function is defined byn#x21;#x21;#x3D;#x5C;begin#x7B;cases#x7D;#x5C;displaystyle 1#x26;n#x3D;-1,0#x5C;#x5C;#x5B;5pt#x5D;#x5C;displaystylen#x5C;times(n-2)#x5C;times(n-4)#x5C;times#x5C;dots#x5C;times 5#x5C;times 3#x5C;times 1#x26;n#x3D;1,3,5,#x5C;dots#x5C;#x5C;#x5B;5pt#x5D;#x5C;displaystylen#x5C;times(n-2)#x5C;times(n-4)#x5C;times#x5C;dots#x5C;times 6#x5C;times 4#x5C;times 2#x26;n#x3D;2,4,6,#x5C;dots#x5C;end#x7B;cases#x7D;",
"type": "quotation"
}
],
"glosses": [
"Synonym of double factorial"
],
"id": "en-semifactorial-en-noun-2BUfGM9n",
"links": [
[
"mathematics",
"mathematics"
],
[
"combinatorics",
"combinatorics"
],
[
"double factorial",
"double factorial#English"
]
],
"raw_glosses": [
"(mathematics, combinatorics, rare) Synonym of double factorial"
],
"synonyms": [
{
"tags": [
"synonym",
"synonym-of"
],
"word": "double factorial"
}
],
"tags": [
"rare"
],
"topics": [
"combinatorics",
"mathematics",
"sciences"
],
"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "mathematics",
"tags": [
"masculine"
],
"word": "semifactorial"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "mathematics",
"tags": [
"masculine"
],
"word": "semifatorial"
},
{
"code": "es",
"lang": "Spanish",
"sense": "mathematics",
"tags": [
"masculine"
],
"word": "semifactorial"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "mathematics",
"tags": [
"common-gender"
],
"word": "semifakultet"
}
]
}
],
"word": "semifactorial"
}
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "semi-",
"3": "factorial"
},
"expansion": "semi- + factorial",
"name": "compound"
}
],
"etymology_text": "semi- + factorial",
"forms": [
{
"form": "semifactorials",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "semifactorial (plural semifactorials)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
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"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
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"English terms with quotations",
"English terms with rare senses",
"en:Combinatorics",
"en:Mathematics"
],
"examples": [
{
"ref": "1942 February, Giulio Racah, “Theory of Complex Spectra. I”, in Physical Review, volume 61, numbers 3–4, →DOI, page 188",
"text": "With the symbol n#x21;#x21; we indicate the semifactorial of n, that is the product 1.3.5#x5C;dotsn if n is odd, and the product 2.4.6#x5C;dotsn if n is even.",
"type": "quotation"
},
{
"ref": "1994 January, Alan Edelman, Eric Kostlan, Michael Shub, “How many eigenvalues of a random matrix are real?”, in Journal of the American Mathematical Society, volume 7, number 1, →DOI, pages 250–251",
"text": "In the formulas above we use the Euler beta function, a Jacobi polynomial evaluated at three, and also the familiar double factorial (also known as the semifactorial) notation defined by n#x21;#x21;#x3D;#x5C;begin#x7B;cases#x7D;#x5C;displaystyle 1#x5C;times 3#x5C;times 5#x5C;times#x5C;dots#x5C;timesn#x26;#x5C;text#x7B;if#x7D;n#x5C;text#x7B;isodd#x7D;,#x5C;#x5C;#x5B;5pt#x5D;#x5C;displaystyle 2#x5C;times 4#x5C;times 6#x5C;times#x5C;dots#x5C;timesn#x26;#x5C;text#x7B;if#x7D;n#x5C;text#x7B;iseven#x7D;.#x5C;end#x7B;cases#x7D;By convention, 0#x21;#x21;#x3D;(-1)#x21;#x21;#x3D;1.",
"type": "quotation"
},
{
"ref": "2009, Keith B. Oldham, Jan C. Myland, Jerome Spanier, An Atlas of Functions, 2nd edition, Springer, →DOI, page 25",
"text": "The double factorial or semifactorial function is defined byn#x21;#x21;#x3D;#x5C;begin#x7B;cases#x7D;#x5C;displaystyle 1#x26;n#x3D;-1,0#x5C;#x5C;#x5B;5pt#x5D;#x5C;displaystylen#x5C;times(n-2)#x5C;times(n-4)#x5C;times#x5C;dots#x5C;times 5#x5C;times 3#x5C;times 1#x26;n#x3D;1,3,5,#x5C;dots#x5C;#x5C;#x5B;5pt#x5D;#x5C;displaystylen#x5C;times(n-2)#x5C;times(n-4)#x5C;times#x5C;dots#x5C;times 6#x5C;times 4#x5C;times 2#x26;n#x3D;2,4,6,#x5C;dots#x5C;end#x7B;cases#x7D;",
"type": "quotation"
}
],
"glosses": [
"Synonym of double factorial"
],
"links": [
[
"mathematics",
"mathematics"
],
[
"combinatorics",
"combinatorics"
],
[
"double factorial",
"double factorial#English"
]
],
"raw_glosses": [
"(mathematics, combinatorics, rare) Synonym of double factorial"
],
"synonyms": [
{
"tags": [
"synonym",
"synonym-of"
],
"word": "double factorial"
}
],
"tags": [
"rare"
],
"topics": [
"combinatorics",
"mathematics",
"sciences"
]
}
],
"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "mathematics",
"tags": [
"masculine"
],
"word": "semifactorial"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "mathematics",
"tags": [
"masculine"
],
"word": "semifatorial"
},
{
"code": "es",
"lang": "Spanish",
"sense": "mathematics",
"tags": [
"masculine"
],
"word": "semifactorial"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "mathematics",
"tags": [
"common-gender"
],
"word": "semifakultet"
}
],
"word": "semifactorial"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-06-01 from the enwiktionary dump dated 2024-05-02 using wiktextract (384852d and db5a844). 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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