Rogers–Ramanujan identities

<http://www.wikidata.org/entity/Q7359380>

Mathematical identities related to basic hypergeometric series

rdfs:label	"Identidades de Rogers-Ramanujan"@pt "Identidades de Rogers-Ramanujan"@pt-br "Identitats de Rogers-Ramanujan"@ca "Rogers-Ramanujan-Identitäten"@de "Rogers–Ramanujan identitateak"@eu "Rogers–Ramanujan identities"@en "Rogers–Ramanujan-identiteter"@da "Rogers–Ramanujan-identiteterna"@sv "identidades de Rogers-Ramanujan"@es "identités de Rogers-Ramanujan"@fr "Тотожність Роджерса — Рамануджана"@uk "همانیهای روجرز - رامانوجان"@fa "ロジャース・ラマヌジャン恒等式"@ja "羅傑斯-拉馬努金恆等式"@zh
skos:altLabel	"ロジャーズ・ラマヌジャン恒等式"@ja
schema:description	"Gleichheit zweier unendlicher Reihen"@de "Identidades matemáticas relacionadas con las series hipergeométricas básicas"@es "Mathematical identities related to basic hypergeometric series"@en "identitats matemàtiques"@ca
schema:dateModified	"2026-08-18T14:12:49+00:00"^^xsd:dateTime
schema:version	2532766679
wikibase:identifiers	5
wikibase:sitelinks	9
wikibase:statements	12
p:P10565	wd:statement/Q7359380-5BCFAD12-30F1-4EA0-9D7A-5EEBD72958DC
p:P1269	wd:statement/Q7359380-1f016775-4bee-b233-2e18-9c0931efb843
p:P138	wd:statement/Q7359380-2d12ee6b-44ce-74d3-5c53-9f3a56af66ba
	wd:statement/Q7359380-d5031478-461d-c891-a6cf-b0d2e109e20f
p:P14541	wd:statement/Q7359380-DED98EBE-3AA7-43EB-86BF-EF710FA44AD8
p:P2534	wd:statement/Q7359380-8cc40f0d-46db-5180-4810-8e8b9d043328
	wd:statement/Q7359380-f02bae0a-402b-d1d1-f886-731ffbde0301
p:P2812	wd:statement/Q7359380-4B5EA357-30D7-47A3-8FD6-DCBB2C44592C
p:P31	wd:statement/Q7359380-9eb501a0-43f3-f9f0-8dcf-71f750a0ed6c
p:P6104	wd:statement/Q7359380-C97BD4B7-0C3C-41F4-B86F-C1314169C3E1
p:P6366	wd:statement/Q7359380-CBCE95B2-AC30-4F1B-8894-D183A4860333
p:P646	wd:statement/Q7359380-43A9E05E-1971-4054-ACEA-E2928EACB1CF
p:direct-normalized/P6366	<https://makg.org/entity/191834802>
wdt:P10565	"57137"
wdt:P1269	hypergeometric series
wdt:P138	Leonard James Rogers
	Srinivasa Ramanujan
wdt:P14541	"2AhGvw"
wdt:P2534	"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>G</mi><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><msup><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>q</mi><mo>;</mo><mi>q</mi><msub><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>q</mi><mo>;</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>5</mn></mrow></msup><msub><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msub><mo stretchy="false">(</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msup><mo>;</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>5</mn></mrow></msup><msub><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mn>1</mn><mo stretchy="false">+</mo><mi>q</mi><mo stretchy="false">+</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo stretchy="false">+</mo><mn>2</mn><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msup><mo stretchy="false">+</mo><mn>2</mn><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>5</mn></mrow></msup><mo stretchy="false">+</mo><mn>3</mn><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>6</mn></mrow></msup><mo stretchy="false">+</mo><mo stretchy="false">⋯</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
	"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>H</mi><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><mi>n</mi></mrow></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>q</mi><mo>;</mo><mi>q</mi><msub><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>;</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>5</mn></mrow></msup><msub><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msub><mo stretchy="false">(</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo>;</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>5</mn></mrow></msup><msub><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mn>1</mn><mo stretchy="false">+</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo stretchy="false">+</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msup><mo stretchy="false">+</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>5</mn></mrow></msup><mo stretchy="false">+</mo><mn>2</mn><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>6</mn></mrow></msup><mo stretchy="false">+</mo><mo stretchy="false">⋯</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P2812	"Rogers-RamanujanIdentities"
wdt:P31	theorem
wdt:P6104	WikiProject Mathematics
wdt:P6366	"191834802"
wdt:P646	"/m/073wyw"

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