<br />
<b>Deprecated</b>:  $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 127] in <b>/var/www/html/w/includes/Debug/MWDebug.php</b> on line <b>372</b><br />
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix owl: <http://www.w3.org/2002/07/owl#> .
@prefix wikibase: <http://wikiba.se/ontology#> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix schema: <http://schema.org/> .
@prefix cc: <http://creativecommons.org/ns#> .
@prefix geo: <http://www.opengis.net/ont/geosparql#> .
@prefix prov: <http://www.w3.org/ns/prov#> .
@prefix wd: <https://drmf-beta.wmflabs.org/entity/> .
@prefix data: <https://drmf-beta.wmflabs.org/wiki/Special:EntityData/> .
@prefix wds: <https://drmf-beta.wmflabs.org/entity/statement/> .
@prefix wdref: <https://drmf-beta.wmflabs.org/reference/> .
@prefix wdv: <https://drmf-beta.wmflabs.org/value/> .
@prefix wdt: <https://drmf-beta.wmflabs.org/prop/direct/> .
@prefix wdtn: <https://drmf-beta.wmflabs.org/prop/direct-normalized/> .
@prefix p: <https://drmf-beta.wmflabs.org/prop/> .
@prefix ps: <https://drmf-beta.wmflabs.org/prop/statement/> .
@prefix psv: <https://drmf-beta.wmflabs.org/prop/statement/value/> .
@prefix psn: <https://drmf-beta.wmflabs.org/prop/statement/value-normalized/> .
@prefix pq: <https://drmf-beta.wmflabs.org/prop/qualifier/> .
@prefix pqv: <https://drmf-beta.wmflabs.org/prop/qualifier/value/> .
@prefix pqn: <https://drmf-beta.wmflabs.org/prop/qualifier/value-normalized/> .
@prefix pr: <https://drmf-beta.wmflabs.org/prop/reference/> .
@prefix prv: <https://drmf-beta.wmflabs.org/prop/reference/value/> .
@prefix prn: <https://drmf-beta.wmflabs.org/prop/reference/value-normalized/> .
@prefix wdno: <https://drmf-beta.wmflabs.org/prop/novalue/> .

data:Q8000 a schema:Dataset ;
	schema:about wd:Q8000 ;
	cc:license <http://creativecommons.org/publicdomain/zero/1.0/> ;
	schema:softwareVersion "1.0.0" ;
	schema:version "45003"^^xsd:integer ;
	schema:dateModified "2020-01-02T12:14:44Z"^^xsd:dateTime ;
	wikibase:statements "6"^^xsd:integer ;
	wikibase:sitelinks "0"^^xsd:integer ;
	wikibase:identifiers "1"^^xsd:integer .

wd:Q8000 a wikibase:Item ;
	wdt:P1 "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><merror><strong class=\"error texerror\">Failed to parse (LaTeXML (experimental; uses MathML): Invalid response (&quot;&quot;) from server &quot;http://latexml:8080/convert/&quot;:): {\\displaystyle \\Liouvillelambda@{n}=\\begin{cases}1,&amp;n=1,\\\\ (-1)^{a_{1}+\\dots+a_{\\nprimesdiv@{n}}},&amp;n&gt;1.\\end{cases}}</strong>\n</merror></math>"^^<http://www.w3.org/1998/Math/MathML> ;
	wdt:P2 "DLMF:27.2.E13" ;
	wdt:P3 wd:Q10603 ;
	wdt:P4 wd:Q12233,
		wd:Q12234,
		wd:Q12236 ;
	p:P1 wds:Q8000-72546375-4126-4356-9F82-A9318BB69B46 .

wds:Q8000-72546375-4126-4356-9F82-A9318BB69B46 a wikibase:Statement,
		wikibase:BestRank ;
	wikibase:rank wikibase:NormalRank ;
	ps:P1 "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><merror><strong class=\"error texerror\">Failed to parse (LaTeXML (experimental; uses MathML): Invalid response (&quot;&quot;) from server &quot;http://latexml:8080/convert/&quot;:): {\\displaystyle \\Liouvillelambda@{n}=\\begin{cases}1,&amp;n=1,\\\\ (-1)^{a_{1}+\\dots+a_{\\nprimesdiv@{n}}},&amp;n&gt;1.\\end{cases}}</strong>\n</merror></math>"^^<http://www.w3.org/1998/Math/MathML> .

wd:Q8000 p:P2 wds:Q8000-7043B385-79C5-493B-958C-DABFF88B8C91 .

wds:Q8000-7043B385-79C5-493B-958C-DABFF88B8C91 a wikibase:Statement,
		wikibase:BestRank ;
	wikibase:rank wikibase:NormalRank ;
	ps:P2 "DLMF:27.2.E13" .

wd:Q8000 p:P3 wds:Q8000-C2053A3E-C688-4C4E-8EED-0F27B00DF4CF .

wds:Q8000-C2053A3E-C688-4C4E-8EED-0F27B00DF4CF a wikibase:Statement,
		wikibase:BestRank ;
	wikibase:rank wikibase:NormalRank ;
	ps:P3 wd:Q10603 .

wd:Q8000 p:P4 wds:Q8000-44D39EA2-EA2D-4024-92F7-F9DCBA52C2DA .

wds:Q8000-44D39EA2-EA2D-4024-92F7-F9DCBA52C2DA a wikibase:Statement,
		wikibase:BestRank ;
	wikibase:rank wikibase:NormalRank ;
	ps:P4 wd:Q12233 ;
	pq:P1 "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><merror><strong class=\"error texerror\">Failed to parse (LaTeXML (experimental; uses MathML): Invalid response (&quot;&quot;) from server &quot;http://latexml:8080/convert/&quot;:): {\\displaystyle \\nprimesdiv@{\\NVar{n}}}</strong>\n</merror></math>"^^<http://www.w3.org/1998/Math/MathML> ;
	pq:P5 "C27.S2.SS1.p1.m6abdec" .

wd:Q8000 p:P4 wds:Q8000-436F4985-5597-4090-9A48-85434ECB68BD .

wds:Q8000-436F4985-5597-4090-9A48-85434ECB68BD a wikibase:Statement,
		wikibase:BestRank ;
	wikibase:rank wikibase:NormalRank ;
	ps:P4 wd:Q12234 ;
	pq:P1 "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><merror><strong class=\"error texerror\">Failed to parse (LaTeXML (experimental; uses MathML): Invalid response (&quot;&quot;) from server &quot;http://latexml:8080/convert/&quot;:): {\\displaystyle n}</strong>\n</merror></math>"^^<http://www.w3.org/1998/Math/MathML> ;
	pq:P5 "C27.S1.XMD4.m1jdec" .

wd:Q8000 p:P4 wds:Q8000-3E40CCEE-84CC-462C-89BB-66A82B68A0B2 .

wds:Q8000-3E40CCEE-84CC-462C-89BB-66A82B68A0B2 a wikibase:Statement,
		wikibase:BestRank ;
	wikibase:rank wikibase:NormalRank ;
	ps:P4 wd:Q12236 ;
	pq:P1 "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><merror><strong class=\"error texerror\">Failed to parse (LaTeXML (experimental; uses MathML): Invalid response (&quot;&quot;) from server &quot;http://latexml:8080/convert/&quot;:): {\\displaystyle a}</strong>\n</merror></math>"^^<http://www.w3.org/1998/Math/MathML> ;
	pq:P5 "C27.S2.XMD2.m1cdec" .

wd:Q8000 rdfs:label "DLMF:27.2.E13"@en ;
	skos:prefLabel "DLMF:27.2.E13"@en ;
	schema:name "DLMF:27.2.E13"@en .

wd:P1 a wikibase:Property ;
	rdfs:label "Defining formula"@en ;
	skos:prefLabel "Defining formula"@en ;
	schema:name "Defining formula"@en ;
	schema:description "The formula defining a mathematical concept or identity"@en ;
	wikibase:propertyType <http://wikiba.se/ontology#Contentmath> ;
	wikibase:directClaim wdt:P1 ;
	wikibase:claim p:P1 ;
	wikibase:statementProperty ps:P1 ;
	wikibase:statementValue psv:P1 ;
	wikibase:qualifier pq:P1 ;
	wikibase:qualifierValue pqv:P1 ;
	wikibase:reference pr:P1 ;
	wikibase:referenceValue prv:P1 ;
	wikibase:novalue wdno:P1 .

p:P1 a owl:ObjectProperty .

psv:P1 a owl:ObjectProperty .

pqv:P1 a owl:ObjectProperty .

prv:P1 a owl:ObjectProperty .

wdt:P1 a owl:DatatypeProperty .

ps:P1 a owl:DatatypeProperty .

pq:P1 a owl:DatatypeProperty .

pr:P1 a owl:DatatypeProperty .

wdno:P1 a owl:Class ;
	owl:complementOf _:b96ec5135b6832e1d84209d72460276b .

_:b96ec5135b6832e1d84209d72460276b a owl:Restriction ;
	owl:onProperty wdt:P1 ;
	owl:someValuesFrom owl:Thing .

wd:P2 a wikibase:Property ;
	rdfs:label "DLMF id"@en ;
	skos:prefLabel "DLMF id"@en ;
	schema:name "DLMF id"@en ;
	schema:description "Link to the DLMF"@en ;
	wikibase:propertyType <http://wikiba.se/ontology#ExternalId> ;
	wikibase:directClaim wdt:P2 ;
	wikibase:claim p:P2 ;
	wikibase:statementProperty ps:P2 ;
	wikibase:statementValue psv:P2 ;
	wikibase:qualifier pq:P2 ;
	wikibase:qualifierValue pqv:P2 ;
	wikibase:reference pr:P2 ;
	wikibase:referenceValue prv:P2 ;
	wikibase:novalue wdno:P2 ;
	wikibase:directClaimNormalized wdtn:P2 ;
	wikibase:statementValueNormalized psn:P2 ;
	wikibase:qualifierValueNormalized pqn:P2 ;
	wikibase:referenceValueNormalized prn:P2 .

p:P2 a owl:ObjectProperty .

psv:P2 a owl:ObjectProperty .

pqv:P2 a owl:ObjectProperty .

prv:P2 a owl:ObjectProperty .

wdt:P2 a owl:DatatypeProperty .

ps:P2 a owl:DatatypeProperty .

pq:P2 a owl:DatatypeProperty .

pr:P2 a owl:DatatypeProperty .

psn:P2 a owl:ObjectProperty .

pqn:P2 a owl:ObjectProperty .

prn:P2 a owl:ObjectProperty .

wdtn:P2 a owl:ObjectProperty .

wdno:P2 a owl:Class ;
	owl:complementOf _:1f05fece3ad482b53eed1f5510da49fa .

_:1f05fece3ad482b53eed1f5510da49fa a owl:Restriction ;
	owl:onProperty wdt:P2 ;
	owl:someValuesFrom owl:Thing .

wd:Q10603 a wikibase:Item ;
	rdfs:label "Liouville’s function"@en ;
	skos:prefLabel "Liouville’s function"@en ;
	schema:name "Liouville’s function"@en .

wd:P3 a wikibase:Property ;
	rdfs:label "Symbols defined"@en ;
	skos:prefLabel "Symbols defined"@en ;
	schema:name "Symbols defined"@en ;
	wikibase:propertyType <http://wikiba.se/ontology#WikibaseItem> ;
	wikibase:directClaim wdt:P3 ;
	wikibase:claim p:P3 ;
	wikibase:statementProperty ps:P3 ;
	wikibase:statementValue psv:P3 ;
	wikibase:qualifier pq:P3 ;
	wikibase:qualifierValue pqv:P3 ;
	wikibase:reference pr:P3 ;
	wikibase:referenceValue prv:P3 ;
	wikibase:novalue wdno:P3 .

p:P3 a owl:ObjectProperty .

psv:P3 a owl:ObjectProperty .

pqv:P3 a owl:ObjectProperty .

prv:P3 a owl:ObjectProperty .

wdt:P3 a owl:ObjectProperty .

ps:P3 a owl:ObjectProperty .

pq:P3 a owl:ObjectProperty .

pr:P3 a owl:ObjectProperty .

wdno:P3 a owl:Class ;
	owl:complementOf _:1086e1c4470bf0a461225f75b332f53e .

_:1086e1c4470bf0a461225f75b332f53e a owl:Restriction ;
	owl:onProperty wdt:P3 ;
	owl:someValuesFrom owl:Thing .

wd:Q12233 a wikibase:Item .

wd:P4 a wikibase:Property ;
	rdfs:label "Symbols used"@en ;
	skos:prefLabel "Symbols used"@en ;
	schema:name "Symbols used"@en ;
	wikibase:propertyType <http://wikiba.se/ontology#WikibaseItem> ;
	wikibase:directClaim wdt:P4 ;
	wikibase:claim p:P4 ;
	wikibase:statementProperty ps:P4 ;
	wikibase:statementValue psv:P4 ;
	wikibase:qualifier pq:P4 ;
	wikibase:qualifierValue pqv:P4 ;
	wikibase:reference pr:P4 ;
	wikibase:referenceValue prv:P4 ;
	wikibase:novalue wdno:P4 .

p:P4 a owl:ObjectProperty .

psv:P4 a owl:ObjectProperty .

pqv:P4 a owl:ObjectProperty .

prv:P4 a owl:ObjectProperty .

wdt:P4 a owl:ObjectProperty .

ps:P4 a owl:ObjectProperty .

pq:P4 a owl:ObjectProperty .

pr:P4 a owl:ObjectProperty .

wdno:P4 a owl:Class ;
	owl:complementOf _:c298799f0cd3665c958b9d4edf0ffbf3 .

_:c298799f0cd3665c958b9d4edf0ffbf3 a owl:Restriction ;
	owl:onProperty wdt:P4 ;
	owl:someValuesFrom owl:Thing .

wd:Q12234 a wikibase:Item .

wd:Q12236 a wikibase:Item .

wd:P5 a wikibase:Property ;
	rdfs:label "xml-id"@en ;
	skos:prefLabel "xml-id"@en ;
	schema:name "xml-id"@en ;
	wikibase:propertyType <http://wikiba.se/ontology#ExternalId> ;
	wikibase:directClaim wdt:P5 ;
	wikibase:claim p:P5 ;
	wikibase:statementProperty ps:P5 ;
	wikibase:statementValue psv:P5 ;
	wikibase:qualifier pq:P5 ;
	wikibase:qualifierValue pqv:P5 ;
	wikibase:reference pr:P5 ;
	wikibase:referenceValue prv:P5 ;
	wikibase:novalue wdno:P5 ;
	wikibase:directClaimNormalized wdtn:P5 ;
	wikibase:statementValueNormalized psn:P5 ;
	wikibase:qualifierValueNormalized pqn:P5 ;
	wikibase:referenceValueNormalized prn:P5 .

p:P5 a owl:ObjectProperty .

psv:P5 a owl:ObjectProperty .

pqv:P5 a owl:ObjectProperty .

prv:P5 a owl:ObjectProperty .

wdt:P5 a owl:DatatypeProperty .

ps:P5 a owl:DatatypeProperty .

pq:P5 a owl:DatatypeProperty .

pr:P5 a owl:DatatypeProperty .

psn:P5 a owl:ObjectProperty .

pqn:P5 a owl:ObjectProperty .

prn:P5 a owl:ObjectProperty .

wdtn:P5 a owl:ObjectProperty .

wdno:P5 a owl:Class ;
	owl:complementOf _:5a6c7a576e39dbbe9a035303bd73cd44 .

_:5a6c7a576e39dbbe9a035303bd73cd44 a owl:Restriction ;
	owl:onProperty wdt:P5 ;
	owl:someValuesFrom owl:Thing .
