@prefix p: <http://www.wikidata.org/prop/> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix schema1: <http://schema.org/> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix wd: <http://www.wikidata.org/entity/> .
@prefix wds: <http://www.wikidata.org/entity/statement/> .
@prefix wdt: <http://www.wikidata.org/prop/direct/> .
@prefix wdtn: <http://www.wikidata.org/prop/direct-normalized/> .
@prefix wikibase: <http://wikiba.se/ontology#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

wd:Q3153996 rdfs:label "Cauchy's estimate"@en,
        "inégalité de Cauchy"@fr,
        "コーシーの不等式"@ja,
        "코시 추정"@ko,
        "ကော်ချီ၏ ခန့်မှန်းချက်"@my,
        "Desigualdades de Cauchy"@pt,
        "неравенство Коши для голоморфных функций"@ru,
        "Cauchyjeva neenakost"@sl,
        "柯西估计"@zh-hans ;
    schema1:dateModified "2026-09-07T08:05:44+00:00"^^xsd:dateTime ;
    schema1:description "bound for the coefficients of the Taylor series of holomorphic functions"@en,
        "inégalité en analyse complexe"@fr,
        "정칙 함수의 테일러 급수의 계수의 계"@ko,
        "全纯函数的泰勒级数的系数的界"@zh-hans ;
    schema1:version 2541582722 ;
    wikibase:identifiers 1 ;
    wikibase:sitelinks 4 ;
    wikibase:statements 19 ;
    skos:altLabel "Cauchy's estimates"@en,
        "Cauchy's inequality"@en,
        "Cauchy's inequality for holomorphic functions"@en,
        "코시 부등식"@ko,
        "Teorema da Majoração de Cauchy"@pt,
        "Teorema da majoração de Cauchy"@pt,
        "柯西不等式"@zh-hans ;
    p:P138 wds:Q3153996-5a143e83-4032-9ece-7f98-8fdc426e1b6b ;
    p:P180 wds:Q3153996-27ae588f-4d48-35c9-c63d-26c3bb33e0bf ;
    p:P1889 wds:Q3153996-21d9084d-4d3e-2557-8663-12a6591a03d8 ;
    p:P2534 wds:Q3153996-bf7f2a62-45a5-0263-421d-8aa41159bf70 ;
    p:P2579 wds:Q3153996-200882f5-486f-9d3e-e689-88f557434165 ;
    p:P2671 wds:Q3153996-6BC398E1-D87A-43A6-B344-686AB6A5BA7F ;
    p:P279 wds:Q3153996-0c096bf0-406b-37b5-681b-ece71ddc1ff8 ;
    p:P6104 wds:Q3153996-B1491E6C-15D1-4FE3-84C4-903053D8D951 ;
    p:P7235 wds:Q3153996-0563b9cb-4985-defa-fa51-67302a22c5c6,
        wds:Q3153996-0974b5e1-4664-afd8-e94f-52a029c3e272,
        wds:Q3153996-22ea3999-4e7d-e79a-2e9f-c039bdd18e25,
        wds:Q3153996-77c83222-48e5-6763-e878-34b6574432d1,
        wds:Q3153996-8aaf33a3-4663-d549-5599-ba19cc6de77a,
        wds:Q3153996-adadee0f-4a81-7ca3-3d1f-65fce148dd80,
        wds:Q3153996-da982774-48f9-a4d7-fd4b-ee0c1141f55f,
        wds:Q3153996-e237e1b7-4cec-1bb2-31cb-28f447d02759,
        wds:Q3153996-ea78532c-4faa-4e35-3aa8-eccbae7dcabd,
        wds:Q3153996-f7f21a87-4f71-b39e-9861-ea9a119cec7f ;
    p:P828 wds:Q3153996-b3d37f42-45a7-63ca-9bc9-b5ba4ebcc281 ;
    wdtn:P2671 <http://g.co/kg/g/1219y4nq> ;
    wdt:P138 wd:Q8814 ;
    wdt:P180 wd:Q207476 ;
    wdt:P1889 wd:Q190546 ;
    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\">&#x2264;</mo><msup><mi>r</mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">&#x2212;</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>&gt;</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 wd:Q193756 ;
    wdt:P2671 "/g/1219y4nq" ;
    wdt:P279 wd:Q28113351 ;
    wdt:P6104 wd:Q8487137 ;
    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 wd:Q913764 .