Lambert W function
multivalued function that is the inverse of the map z ↦ z exp(z)
| rdfs:label |
"Lambert W function"@en
|
|
skos:alt |
"omega function"@en
"product logarithm"@en
|
| schema:description |
"multivalued function that is the inverse of the map z ↦ z exp(z)"@en
|
|
schema:date |
"2026-09-06T06:49:10+00:00"^^xsd:dateTime |
| schema:version | 2540907960 |
| wikibase:identifiers | 8 |
| wikibase:sitelinks | 27 |
| wikibase:statements | 20 |
| p:P10283 | wd:statement/Q429331-ECD53316-F316-4476-B3D9-376C30FB6615 |
| p:P10969 | wd:statement/Q429331-0ab8fbd2-4ca7-db67-0c6d-58399c5794d5 |
| p:P1171 | wd:statement/Q429331-ed8a9ec2-4cf6-4d93-cbd7-c7cefecae8bc |
| p:P138 | wd:statement/q429331-0e32262b-463d-6801-dfc8-36103acba2e9 |
| p:P1482 | wd:statement/Q429331-65d88f96-41a8-7459-904e-d397cdf34e62 |
| p:P18 | wd:statement/Q429331-dad4f21e-4545-4467-e915-6c2d02cd5c59 |
| p:P2534 | wd:statement/Q429331-c57efa39-4d75-799b-bd09-87ca9651e53b |
| p:P2812 | wd:statement/Q429331-7d3458e1-4645-b577-c1de-288acf836b07 |
| p:P31 | wd:statement/Q429331-203b81cf-43bb-13a5-a57e-48c750dc632a |
| p:P3417 | wd:statement/Q429331-D4A6442C-6C8D-4CA6-B3A7-C0B78D60B28F |
| p:P373 | wd:statement/Q429331-AEA5BDE5-FF26-48B1-BDAC-4603D3183F57 |
| p:P4215 | wd:statement/Q429331-3d1344d0-41c5-e52b-b586-1aaabaefbaa9 |
| p:P6104 | wd:statement/Q429331-047E576A-15C7-495C-9E44-61BECBA16D66 |
| p:P6366 | wd:statement/Q429331-3D99BFA2-1729-49A9-A042-B1CB3486A050 |
| p:P646 | wd:statement/Q429331-558934F4-0A37-4CEC-A8B0-4A58B4696A2F |
| p:P6781 | wd:statement/Q429331-64f96c2b-4c89-9a29-a4d8-b1c2ed9b9001 |
| p:P7235 | wd:statement/Q429331-58b7c099-4228-12d5-8905-ee0330055bcc |
| wd:statement/Q429331-72c40e51-4155-39f0-9911-7c06845a5fc2 | |
| wd:statement/Q429331-90d8baa5-4cbd-7300-14ea-b15e19eddb0b | |
| p:P8885 | wd:statement/Q429331-d459f861-492b-3ca2-f6f7-539627f1473e |
|
p:direct- |
<https:/ |
| wdt:P10283 | "C130924491" |
| wdt:P10969 | "<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"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd><msub><mi>W</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mtd><mtd><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>1</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"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mi>n</mi><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">!</mo></mrow></mrow></mfrac></mrow><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">=</mo><mi>x</mi><mo stretchy="false">−</mo><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mstyle displaystyle="false" scriptlevel="0"><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></mstyle></mrow><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mstyle displaystyle="false" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>8</mn></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></mfrac></mrow></mstyle></mrow><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msup><mo stretchy="false">+</mo><mo stretchy="false">…</mo></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P1171 | Newton's method |
| wdt:P138 | Johann Heinrich Lambert |
| wdt:P1482 |
<https:/ |
| wdt:P18 |
<http:/ |
| 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>z</mi><mo stretchy="false">=</mo><mi>W</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><mi>exp</mi><mo>⁡</mo><mi>W</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2812 | "LambertW-Function" |
| wdt:P31 | function |
| wdt:P3417 | "Lambert-W-Function" |
| wdt:P373 | "Lambert W function" |
| wdt:P4215 | "Lambert W-function" |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "130924491" |
| wdt:P646 | "/m/0m_5j" |
| wdt:P6781 | "Definition:Lambert_W_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"><mi>W</mi><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"><mi>exp</mi></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>z</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| wdt:P8885 | "람베르트 W 함수" |
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