DLMF:14.8.E9 (Q4783): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\NVar{z}}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2afdec
Property / Symbols used
 
Property / Symbols used: Euler’s constant / rank
 
Normal rank
Property / Symbols used: Euler’s constant / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerConstant}

\EulerConstant
Property / Symbols used: Euler’s constant / qualifier
 
xml-id: C5.S2.E3.m2aadec
Property / Symbols used
 
Property / Symbols used: psi (or digamma) function / rank
 
Normal rank
Property / Symbols used: psi (or digamma) function / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{\NVar{z}}}

\digamma@{\NVar{z}}
Property / Symbols used: psi (or digamma) function / qualifier
 
xml-id: C5.S2.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11597 / rank
 
Normal rank
Property / Symbols used: Q11597 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreOlverQ[]{\NVar{\nu}}@{\NVar{z}}=\assLegendreOlverQ[0]{\nu}@{z}}

\assLegendreOlverQ[]{\NVar{\nu}}@{\NVar{z}}=\assLegendreOlverQ[0]{\nu}@{z}
Property / Symbols used: Q11597 / qualifier
 
xml-id: C14.S2.SS2.p2.m6adec
Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1hdec
Property / Symbols used
 
Property / Symbols used: Q11590 / rank
 
Normal rank
Property / Symbols used: Q11590 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu}

\nu
Property / Symbols used: Q11590 / qualifier
 
xml-id: C14.S1.XMD8.m1hdec

Latest revision as of 00:33, 2 January 2020

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DLMF:14.8.E9
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreOlverQ[]{\nu}@{x}=-\frac{\ln@{x-1}}{2\EulerGamma@{\nu+1}}+\frac{\frac{1}{2}\ln@@{2}-\EulerConstant-\digamma@{\nu+1}}{\EulerGamma@{\nu+1}}+\bigO@{x-1},}
    0 references
    DLMF id
    DLMF:14.8.E9
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu\neq-1,-2,-3,\dots}
    0 references
    Symbols used
    order not exceeding
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \bigO@{\NVar{x}}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
    gamma function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\NVar{z}}}
    xml-id
    C5.S2.E1.m2afdec
    0 references
    Euler’s constant
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerConstant}
    xml-id
    C5.S2.E3.m2aadec
    0 references
    psi (or digamma) function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{\NVar{z}}}
    xml-id
    C5.S2.E2.m2aadec
    0 references
    principal branch of logarithm function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q11597
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreOlverQ[]{\NVar{\nu}}@{\NVar{z}}=\assLegendreOlverQ[0]{\nu}@{z}}
    xml-id
    C14.S2.SS2.p2.m6adec
    0 references
    Q11589
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}
    xml-id
    C14.S1.XMD1.m1hdec
    0 references
    Q11590
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu}
    xml-id
    C14.S1.XMD8.m1hdec
    0 references
     
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