SHMARQL

Legendre polynomial

<http://www.wikidata.org/entity/Q215405>

solutions to Legendre's differential equation
rdfs:label
"Legendre polynomial"@en
skos:altLabel
"legendre polynomials"@en
schema:description
"solutions to Legendre's differential equation"@en
schema:dateModified "2026-06-15T18:38:32+00:00"^^xsd:dateTime
schema:version 2506397217
wikibase:identifiers 20
wikibase:sitelinks 35
wikibase:statements 40
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p:P9030 wd:statement/Q215405-1cdd28a0-408d-1673-27da-a857a89e2b87
p:direct-normalized/P2163 <http://id.worldcat.org/fast/995591>
p:direct-normalized/P227 <https://d-nb.info/gnd/4333222-5>
p:direct-normalized/P244 <http://id.loc.gov/authorities/names/sh85075779>
p:direct-normalized/P268 <http://data.bnf.fr/ark:/12148/cb12122983h#about>
p:direct-normalized/P269 <http://www.idref.fr/029649501/id>
p:direct-normalized/P349 <http://id.ndl.go.jp/auth/ndlna/00567364>
p:direct-normalized/P508 <http://purl.org/bncf/tid/38392>
p:direct-normalized/P6366 <https://makg.org/entity/111458787>
wdt:P10283 "C111458787"
wdt:P1036 "515.55"
wdt:P1343 ISO 80000-2:2019 Quantities and units — Part 2: Mathematics
Great Soviet Encyclopedia (1926–1947)
wdt:P13591 "concept/fb07b68f-e97d-47b0-832d-1a750dd9afa2"
wdt:P138 Adrien-Marie Legendre
wdt:P1889 Legendre function
associated Legendre polynomials
wdt:P2163 "995591"
wdt:P227 "4333222-5"
wdt:P244 "sh85075779"
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"><msub><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">P</mi></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><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"><msup><mn>2</mn><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mi>n</mi><mo stretchy="false">!</mo></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">d</mi></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">d</mi></mrow><msup><mi>z</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup></mrow></mrow></mfrac></mrow><mo stretchy="false">(</mo><msup><mi>z</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">&#x2212;</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo>,</mo><mi>n</mi><mo stretchy="false">&#x2208;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>𝖭</mi></mrow></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P268 "12122983h"
wdt:P269 "029649501"
wdt:P279 polynomial sequence
Gegenbauer polynomials
orthogonal polynomials
wdt:P2812 "LegendrePolynomial"
wdt:P2924 "2137289"
wdt:P31 Legendre function
mathematical concept
special function
wdt:P3417 "Legendre-Polynomials"
wdt:P349 "00567364"
wdt:P373 "Legendre polynomials"
wdt:P3827 "legendre-polynomials"
wdt:P4215 "Legendre polynomial"
wdt:P508 "38392"
wdt:P575 "1782-01-01T00:00:00+00:00"^^xsd:dateTime
wdt:P61 Adrien-Marie Legendre
wdt:P6104 WikiProject Mathematics
wdt:P6366 "111458787"
wdt:P646 "/m/0pkk3"
wdt:P691 "ph135787"
wdt:P7235 "<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>n</mi><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"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>𝖭</mi></mrow></mrow></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"><msub><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">P</mi></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P8189 "987007560402505171"
wdt:P8313 "Legendre-polynomier"
wdt:P9030 Legendre differential equation
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