Legendre function
solutions of Legendre's differential equation
| rdfs:label |
"Legendre function"@en
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skos:alt |
"legendresche Funktion"@de |
| schema:description |
"solutions of Legendre's differential equation"@en
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schema:date |
"2026-09-03T16:40:03+00:00"^^xsd:dateTime |
| schema:version | 2539752541 |
| wikibase:identifiers | 13 |
| wikibase:sitelinks | 5 |
| wikibase:statements | 20 |
| p:P10283 | wd:statement/Q17098449-0F55A86C-46A9-4CA4-880A-6C490F84C74E |
| p:P13591 | wd:statement/Q17098449-746B1A8B-9BE6-42FB-B944-C37F68BD80B0 |
| p:P1889 | wd:statement/Q17098449-54ce61db-4bb5-d200-0f08-8e2da14bb5a4 |
| wd:statement/Q17098449-f8d6970c-4534-081b-901b-d7993fae2861 | |
| p:P2163 | wd:statement/Q17098449-1D01055B-97AB-4643-B400-6AC2291DB168 |
| p:P227 | wd:statement/Q17098449-E71FB1CC-6D00-49E8-8846-74FE6378B89A |
| p:P244 | wd:statement/Q17098449-7C901BA7-11D1-4D06-9D3A-E9ED4824731E |
| p:P2534 | wd:statement/Q17098449-50473bf8-4d4c-fa81-0403-0aee7deb3c8c |
| wd:statement/Q17098449-555c8eb0-4282-bafb-57f1-6d72f1884698 | |
| p:P268 | wd:statement/Q17098449-3C69BE20-11AB-4729-A876-15676B8472F7 |
| p:P269 | wd:statement/Q17098449-03E80966-7A30-46A4-BAEF-82AB370BC5BF |
| p:P279 | wd:statement/Q17098449-00ce8931-4c09-b77d-c765-fd23d2fd1aa8 |
| wd:statement/Q17098449-68de6e88-4807-6e78-55ae-ec98c044de6a | |
| p:P3827 | wd:statement/Q17098449-B9E6BFDB-59B7-4FC7-97F5-C04DE2FD9463 |
| p:P6104 | wd:statement/Q17098449-54075162-F4C8-436B-8AD2-096D1A4F98F7 |
| p:P6366 | wd:statement/Q17098449-67FD7CCD-522E-4482-BB5D-9923D1B5AE31 |
| p:P646 | wd:statement/Q17098449-EAD507D2-AD74-414C-A9E7-31647D42A336 |
| p:P7293 | wd:statement/Q17098449-38d730a1-40c1-6a0a-159d-b1a78e613cac |
| p:P8189 | wd:statement/Q17098449-38E54138-2863-417E-B9D1-2AAA08D929DF |
| p:P950 | wd:statement/Q17098449-3019E020-5799-4B56-AF00-C1A64E3E2597 |
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p:direct- |
<http:/ |
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p:direct- |
<https:/ |
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p:direct- |
<http:/ |
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p:direct- |
<http:/ |
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p:direct- |
<http:/ |
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p:direct- |
<https:/ |
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p:direct- |
<https:/ |
| wdt:P10283 | "C153262748" |
| wdt:P13591 | "concept/24ef0893-c63e-4f5f-b4c3-89b4755c0697" |
| wdt:P1889 | Legendre chi function |
| Legendre polynomial | |
| wdt:P2163 | "995590" |
| wdt:P227 | "4332825-8" |
| wdt:P244 | "sh85075778" |
| 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><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>λ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msubsup><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"><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">−</mo><mi>μ</mi><mo stretchy="false">)</mo></mrow></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mo stretchy="false">+</mo><mi>z</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mo stretchy="false">−</mo><mi>z</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><mo lspace="0" rspace="0">/</mo><mn>2</mn></mrow></mrow></msup><msub><mspace width="0.167em"></mspace><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo stretchy="false">−</mo><mi>λ</mi><mo>,</mo><mi>λ</mi><mo stretchy="false">+</mo><mn>1</mn><mo>;</mo><mn>1</mn><mo stretchy="false">−</mo><mi>μ</mi><mo>;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mo stretchy="false">−</mo><mi>z</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>,</mo><mspace width="2em"></mspace><mrow data-mjx-texclass="ORD"><mtext>for </mtext></mrow><mtext> </mtext><mo stretchy="false">|</mo><mn>1</mn><mo stretchy="false">−</mo><mi>z</mi><mo stretchy="false">|</mo><mo><</mo><mn>2</mn></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><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>λ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msubsup><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"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mi>π</mi></msqrt></mrow><mtext> </mtext><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">+</mo><mi>μ</mi><mo stretchy="false">+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mn>2</mn><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>λ</mi><mo stretchy="false">+</mo><mn>1</mn></mrow></mrow></msup><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">+</mo><mn>3</mn><mo lspace="0" rspace="0">/</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>μ</mi><mi>π</mi></mrow></mrow></msup><mo stretchy="false">(</mo><msup><mi>z</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><mo lspace="0" rspace="0">/</mo><mn>2</mn></mrow></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mi>z</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>λ</mi><mo stretchy="false">+</mo><mi>μ</mi><mo stretchy="false">+</mo><mn>1</mn></mrow></mrow></msup></mrow></mfrac></mrow><msub><mspace width="0.167em"></mspace><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>λ</mi><mo stretchy="false">+</mo><mi>μ</mi><mo stretchy="false">+</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>λ</mi><mo stretchy="false">+</mo><mi>μ</mi><mo stretchy="false">+</mo><mn>2</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo>;</mo><mi>λ</mi><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo>;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mi>z</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>,</mo><mspace width="2em"></mspace><mrow data-mjx-texclass="ORD"><mtext>for</mtext></mrow><mtext> </mtext><mtext> </mtext><mo stretchy="false">|</mo><mi>z</mi><mo stretchy="false">|</mo><mo>></mo><mn>1</mn></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| wdt:P268 | "12259775t" |
| wdt:P269 | "031369499" |
| wdt:P279 | mathematical concept |
| special function | |
| wdt:P3827 | "legendre-functions" |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "153262748" |
| wdt:P646 | "/m/0bwhl6d" |
| wdt:P7293 | "9814574596405606" |
| wdt:P8189 | "987007560402605171" |
| wdt:P950 | "XX536155" |
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