Cauchy's estimate
bound for the coefficients of the Taylor series of holomorphic functions
| rdfs:label |
"Cauchy's estimate"@en
|
|
skos:alt |
"Cauchy's estimates"@en
"Cauchy's inequality"@en
"Cauchy's inequality for holomorphic functions"@en
|
| schema:description |
"bound for the coefficients of the Taylor series of holomorphic functions"@en
|
|
schema:date |
"2026-09-07T08:05:44+00:00"^^xsd:dateTime |
| schema:version | 2541582722 |
| wikibase:identifiers | 1 |
| wikibase:sitelinks | 4 |
| wikibase:statements | 19 |
| p:P138 | wd:statement/Q3153996-5a143e83-4032-9ece-7f98-8fdc426e1b6b |
| p:P180 | wd:statement/Q3153996-27ae588f-4d48-35c9-c63d-26c3bb33e0bf |
| p:P1889 | wd:statement/Q3153996-21d9084d-4d3e-2557-8663-12a6591a03d8 |
| p:P2534 | wd:statement/Q3153996-bf7f2a62-45a5-0263-421d-8aa41159bf70 |
| p:P2579 | wd:statement/Q3153996-200882f5-486f-9d3e-e689-88f557434165 |
| p:P2671 | wd:statement/Q3153996-6BC398E1-D87A-43A6-B344-686AB6A5BA7F |
| p:P279 | wd:statement/Q3153996-0c096bf0-406b-37b5-681b-ece71ddc1ff8 |
| p:P6104 | wd:statement/Q3153996-B1491E6C-15D1-4FE3-84C4-903053D8D951 |
| p:P7235 | wd:statement/Q3153996-0563b9cb-4985-defa-fa51-67302a22c5c6 |
| wd:statement/Q3153996-0974b5e1-4664-afd8-e94f-52a029c3e272 | |
| wd:statement/Q3153996-22ea3999-4e7d-e79a-2e9f-c039bdd18e25 | |
| wd:statement/Q3153996-77c83222-48e5-6763-e878-34b6574432d1 | |
| wd:statement/Q3153996-8aaf33a3-4663-d549-5599-ba19cc6de77a | |
| wd:statement/Q3153996-adadee0f-4a81-7ca3-3d1f-65fce148dd80 | |
| wd:statement/Q3153996-da982774-48f9-a4d7-fd4b-ee0c1141f55f | |
| wd:statement/Q3153996-e237e1b7-4cec-1bb2-31cb-28f447d02759 | |
| wd:statement/Q3153996-ea78532c-4faa-4e35-3aa8-eccbae7dcabd | |
| wd:statement/Q3153996-f7f21a87-4f71-b39e-9861-ea9a119cec7f | |
| p:P828 | wd:statement/Q3153996-b3d37f42-45a7-63ca-9bc9-b5ba4ebcc281 |
|
p:direct- |
<http:/ |
| wdt:P138 | Augustin-Louis Cauchy |
| wdt:P180 | holomorphic function |
| wdt:P1889 | Cauchy–Schwarz inequality |
| 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"><mo stretchy="false">|</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">|</mo><mo stretchy="false">≤</mo><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi>n</mi></mrow></mrow></msup><munder><mi>sup</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">|</mo><mi>z</mi><mo stretchy="false">|</mo><mo stretchy="false">=</mo><mi>r</mi></mrow></mrow></munder><mo stretchy="false">|</mo><mi>f</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><mo stretchy="false">|</mo></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 mathvariant="normal">∀</mi><mi>a</mi><mo stretchy="false">∈</mo><mrow data-mjx-texclass="ORD"><mi>ℂ</mi></mrow><mi mathvariant="normal">∀</mi><mi>r</mi><mo>></mo><mn>0</mn><mi mathvariant="normal">∀</mi><mi>f</mi><mo stretchy="false">∈</mo><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">ℋ</mi></mrow><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>B</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mi>a</mi><mo>,</mo><mi>r</mi><mo stretchy="false">)</mo><mo>,</mo><mrow data-mjx-texclass="ORD"><mi>ℂ</mi></mrow><mo stretchy="false">)</mo><mi mathvariant="normal">∀</mi><mi>n</mi><mo stretchy="false">∈</mo><mrow data-mjx-texclass="ORD"><mi>ℕ</mi></mrow><mo stretchy="false">:</mo><mo stretchy="false">|</mo><msup><mi>f</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo stretchy="false">|</mo><mo stretchy="false">≤</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">!</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup></mrow></mfrac></mrow><munder><mi>sup</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>z</mi><mo stretchy="false">∈</mo><mi>∂</mi><mi>B</mi><mo stretchy="false">(</mo><mi>a</mi><mo>,</mo><mi>r</mi><mo stretchy="false">)</mo></mrow></mrow></munder><mo stretchy="false">|</mo><mi>f</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><mo stretchy="false">|</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| wdt:P2579 | complex analysis |
| wdt:P2671 | "/g/1219y4nq" |
| wdt:P279 | inequality |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P7235 | "<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>B</mi><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mo>,</mo><mo stretchy="false">−</mo><mo stretchy="false">)</mo></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>sup</mi></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>∂</mi></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"><mo stretchy="false">!</mo></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"><mo stretchy="false">(</mo><mo stretchy="false">−</mo><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></mrow></msup></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"><mo stretchy="false">|</mo><mo stretchy="false">−</mo><mo stretchy="false">|</mo></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"><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">ℋ</mi></mrow><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mo>,</mo><mo stretchy="false">−</mo><mo stretchy="false">)</mo></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"><mrow data-mjx-texclass="ORD"><mi>ℂ</mi></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"><mrow data-mjx-texclass="ORD"><mi>ℕ</mi></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"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>B</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mo>,</mo><mo stretchy="false">−</mo><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| wdt:P828 | Cauchy's integral formula |
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