Lerch transcendent
special mathematical function given by the series ∑_{n=0}^∞ z^n/(n+α)^s
| rdfs:label |
"Lerch transcendent"@en
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skos:alt |
"Lerch zeta function"@en
|
| schema:description |
"special mathematical function given by the series ∑_{n=0}^∞ z^n/(n+α)^s"@en
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schema:date |
"2026-03-17T23:39:58+00:00"^^xsd:dateTime |
| schema:version | 2473084556 |
| wikibase:identifiers | 4 |
| wikibase:sitelinks | 10 |
| wikibase:statements | 10 |
| p:P138 | wd:statement/Q1546155-1fbf4781-4938-e9e2-d046-345eba4b9917 |
| wd:statement/Q1546155-f7d5ef6f-489d-203e-96c1-44aec12790ab | |
| p:P2534 | wd:statement/Q1546155-71c9a1c9-4049-10ab-188c-3ad79ad7f987 |
| p:P2812 | wd:statement/Q1546155-BD5274F0-1A19-44ED-87BB-DAE7BB97292A |
| p:P31 | wd:statement/Q1546155-504ead41-466d-a213-82a0-e63ce975c18d |
| wd:statement/Q1546155-c00cf363-4534-d941-62c9-aa6fd223bd2d | |
| p:P6104 | wd:statement/Q1546155-DD360227-8E0C-464B-ADB2-95B1F46B2B4F |
| p:P6366 | wd:statement/Q1546155-F03E8D4A-A541-4A78-9F7C-0431E445411F |
| p:P646 | wd:statement/Q1546155-6BEFDA2F-C72E-4D9F-9502-9B3E6D4B569C |
| p:P6781 | wd:statement/Q1546155-b063db38-42f4-9a56-cd56-8d93c5ef9d02 |
|
p:direct- |
<https:/ |
| wdt:P138 | Adolf Hurwitz |
| Mathias Lerch | |
| 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>L</mi><mo stretchy="false">(</mo><mi>λ</mi><mo>,</mo><mi>α</mi><mo>,</mo><mi>s</mi><mo stretchy="false">)</mo><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>0</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"><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>π</mi><mi>i</mi><mi>λ</mi><mi>n</mi></mrow></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">+</mo><mi>α</mi><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mi>s</mi></mrow></msup></mrow></mrow></mfrac></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| "<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>Φ</mi><mo stretchy="false">(</mo><mi>z</mi><mo>,</mo><mi>α</mi><mo>,</mo><mi>s</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><munderover><mo movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>z</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">+</mo><mi>α</mi><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mi>s</mi></mrow></msup></mrow></mrow></mfrac></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| wdt:P2812 | "LerchTranscendent" |
| wdt:P31 | function |
| special function | |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "2781367352" |
| wdt:P646 | "/m/04v7tx" |
| wdt:P6781 | "Definition:Lerch_Transcendent" |
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