associated Legendre polynomials
canonical solutions of the general Legendre equation
| rdfs:label |
"associated Legendre polynomials"@en
|
|
skos:alt |
"associated Legendre function"@en
"associated Legendre polynomial"@en
|
| schema:description |
"canonical solutions of the general Legendre equation"@en
|
|
schema:date |
"2026-09-06T17:40:33+00:00"^^xsd:dateTime |
| schema:version | 2541223472 |
| wikibase:identifiers | 7 |
| wikibase:sitelinks | 19 |
| wikibase:statements | 22 |
| p:P10283 | wd:statement/Q228376-AFBEDA6A-F429-48F4-818C-809A74408BD2 |
| p:P10376 | wd:statement/Q228376-e30f7bda-4911-1a41-ae1f-621f3a60387d |
| p:P1343 | wd:statement/Q228376-8e0adf5c-4b0b-6731-fb53-a1ec5f93b462 |
| p:P138 | wd:statement/Q228376-e24e9fb4-4b03-338e-366b-aacb33227b5a |
| p:P18 | wd:statement/Q228376-204f40e5-492b-21b4-7e5c-0990cb1b0ee6 |
| wd:statement/Q228376-29825d46-4828-5d52-97ed-3e3a36fe520e | |
| wd:statement/Q228376-63cb29ec-4759-63b8-3fce-820472b122d2 | |
| p:P1889 | wd:statement/Q228376-f74f59d0-402d-c32d-302b-84fa3e677114 |
| p:P227 | wd:statement/Q228376-360FA910-0222-45B5-9E9E-B8ED58AC2CFB |
| p:P2534 | wd:statement/Q228376-30b843dd-4de8-39fb-e41d-4ed3cae51a6a |
| p:P279 | wd:statement/Q228376-28DE5D81-546A-4FC2-9B76-736F0466C17F |
| wd:statement/Q228376-546D5607-AAE7-4289-A0FC-256630E61BCC | |
| p:P2812 | wd:statement/Q228376-A88B1A84-F3F5-455C-A090-EF03075AC62F |
| p:P31 | wd:statement/Q228376-6ce9dd70-4ab2-ef90-5d39-aee00e53a8be |
| wd:statement/Q228376-9ed25f64-4af9-12ad-1e50-19a22923db54 | |
| p:P6104 | wd:statement/Q228376-FB040320-58D0-4675-9702-3A382EEDD9D3 |
| p:P6366 | wd:statement/Q228376-3BB8674B-5CA0-479D-B705-702FD8D5C250 |
| p:P646 | wd:statement/Q228376-8562FA1B-AD06-4007-ABE4-5037669B529F |
| p:P6781 | wd:statement/Q228376-822b93fe-4de1-243c-545e-efefebcb6295 |
| p:P7235 | wd:statement/Q228376-253010c0-483c-96cb-c0d0-471a0c25ac16 |
| wd:statement/Q228376-2e49018e-46f2-ece1-d970-acf9ef6caf6d | |
| wd:statement/Q228376-edd6e16c-45a3-44e0-836d-db290203b2d9 | |
|
p:direct- |
<https:/ |
|
p:direct- |
<https:/ |
| wdt:P10283 | "C36956377" |
| wdt:P10376 | "mathematics/associated-legendre-function" |
| wdt:P1343 | ISO 80000-2:2019 Quantities and units — Part 2: Mathematics |
| wdt:P138 | Adrien-Marie Legendre |
| wdt:P18 |
<http:/ |
|
<http:/ |
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|
<http:/ |
|
| wdt:P1889 | Legendre polynomial |
| wdt:P227 | "4333224-9" |
| 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"><msubsup><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">P</mi></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msup><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">−</mo><msup><mi>z</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mo lspace="0" rspace="0">/</mo><mn>2</mn></mrow></mrow></msup><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>m</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>m</mi></mrow></msup></mrow></mrow></mfrac></mrow><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>,</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo stretchy="false">∈</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>𝖭</mi></mrow></mrow><mo>,</mo><mi>m</mi><mo stretchy="false">≤</mo><mi>n</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P279 | function |
| special function | |
| wdt:P2812 | "AssociatedLegendrePolynomial" |
| wdt:P31 | Legendre function |
| mathematical concept | |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "36956377" |
| wdt:P646 | "/m/042nzg" |
| wdt:P6781 | "Associated_Legendre_Function" |
| 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"><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 | |
| "<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"><msubsup><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">P</mi></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
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