DLMF:25.11.E19 (Q7693): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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Property / constraint
 

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s\neq 1}

s\neq 1
Property / constraint: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s\neq 1} / rank
 
Normal rank
Property / constraint
 

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a>0}

a>0
Property / constraint: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a>0} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q11109 / rank
 
Normal rank
Property / Symbols used: Q11109 / qualifier
 
Defining formula:

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

\BernoullinumberB{\NVar{n}}
Property / Symbols used: Q11109 / qualifier
 
xml-id: C24.S2.SS1.m1abdec
Property / Symbols used
 
Property / Symbols used: Hurwitz zeta function / rank
 
Normal rank
Property / Symbols used: Hurwitz zeta function / qualifier
 
Defining formula:

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

\Hurwitzzeta@{\NVar{s}}{\NVar{a}}
Property / Symbols used: Hurwitz zeta function / qualifier
 
xml-id: C25.S11.E1.m2atdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1acdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

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

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3acdec
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: Q11110 / rank
 
Normal rank
Property / Symbols used: Q11110 / qualifier
 
Defining formula:

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

\perBernoulliB{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11110 / qualifier
 
xml-id: C24.S2.SS3.m1abdec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

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

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1agdec
Property / Symbols used
 
Property / Symbols used: Q12152 / rank
 
Normal rank
Property / Symbols used: Q12152 / qualifier
 
Defining formula:

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

x
Property / Symbols used: Q12152 / qualifier
 
xml-id: C25.S1.XMD5.m1edec
Property / Symbols used
 
Property / Symbols used: Q12161 / rank
 
Normal rank
Property / Symbols used: Q12161 / qualifier
 
Defining formula:

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

a
Property / Symbols used: Q12161 / qualifier
 
xml-id: C25.S1.XMD6.m1qdec
Property / Symbols used
 
Property / Symbols used: Q12149 / rank
 
Normal rank
Property / Symbols used: Q12149 / qualifier
 
Defining formula:

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

s
Property / Symbols used: Q12149 / qualifier
 
xml-id: C25.S1.XMD7.m1ndec
Property / Symbols used
 
Property / Symbols used: Q12162 / rank
 
Normal rank
Property / Symbols used: Q12162 / qualifier
 
Defining formula:

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

k
Property / Symbols used: Q12162 / qualifier
 
xml-id: C25.S11.XMD2.m1dec

Latest revision as of 13:39, 2 January 2020

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English
DLMF:25.11.E19
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Hurwitzzeta'@{s}{a}=-\frac{\ln@@{a}}{a^{s}}\left(\frac{1}{2}+\frac{a}{s-1}\right)-\frac{a^{1-s}}{(s-1)^{2}}+\frac{s(s+1)}{2}\int_{0}^{\infty}\frac{(\perBernoulliB{2}@{x}-\BernoullinumberB{2})\ln@{x+a}}{(x+a)^{s+2}}\diff{x}-\frac{(2s+1)}{2}\int_{0}^{\infty}\frac{\perBernoulliB{2}@{x}-\BernoullinumberB{2}}{(x+a)^{s+2}}\diff{x},}
    0 references
    DLMF id
    DLMF:25.11.E19
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{s}>-1}
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s\neq 1}
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a>0}
    0 references
    Symbols used
    Q11109
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BernoullinumberB{\NVar{n}}}
    xml-id
    C24.S2.SS1.m1abdec
    0 references
    Hurwitz zeta function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Hurwitzzeta@{\NVar{s}}{\NVar{a}}}
    xml-id
    C25.S11.E1.m2atdec
    0 references
    Q10770
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \diff{\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    Q10771
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int}
    xml-id
    C1.S4.SS4.m3acdec
    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
    Q11110
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \perBernoulliB{\NVar{n}}@{\NVar{x}}}
    xml-id
    C24.S2.SS3.m1abdec
    0 references
    Q10811
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@}
    xml-id
    C1.S9.E2.m1agdec
    0 references
    Q12152
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}
    xml-id
    C25.S1.XMD5.m1edec
    0 references
    Q12161
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a}
    xml-id
    C25.S1.XMD6.m1qdec
    0 references
    Q12149
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s}
    xml-id
    C25.S1.XMD7.m1ndec
    0 references
    Q12162
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
    xml-id
    C25.S11.XMD2.m1dec
    0 references
     
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