DLMF:25.16.E6 (Q7761): Difference between revisions

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‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
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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.m2adec
Property / Symbols used
 
Property / Symbols used: Q12169 / rank
 
Normal rank
Property / Symbols used: Q12169 / qualifier
 
Defining formula:

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

\EulersumH@{\NVar{s}}
Property / Symbols used: Q12169 / qualifier
 
xml-id: C25.S16.SS2.p1.m1aadec
Property / Symbols used
 
Property / Symbols used: Riemann zeta function / rank
 
Normal rank
Property / Symbols used: Riemann zeta function / qualifier
 
Defining formula:

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

\Riemannzeta@{\NVar{s}}
Property / Symbols used: Riemann zeta function / qualifier
 
xml-id: C25.S2.E1.m2aadec
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.m1adec
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.m3adec
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.m1adec
Property / Symbols used
 
Property / Symbols used: Q12150 / rank
 
Normal rank
Property / Symbols used: Q12150 / qualifier
 
Defining formula:

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

k
Property / Symbols used: Q12150 / qualifier
 
xml-id: C25.S1.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q12148 / rank
 
Normal rank
Property / Symbols used: Q12148 / qualifier
 
Defining formula:

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

n
Property / Symbols used: Q12148 / qualifier
 
xml-id: C25.S1.XMD3.m1adec
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.m1ddec
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.m1adec

Latest revision as of 01:06, 2 January 2020

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DLMF:25.16.E6
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulersumH@{s}=-\Riemannzeta'@{s}+\EulerConstant\Riemannzeta@{s}+\frac{1}{2}\Riemannzeta@{s+1}+\sum_{r=1}^{k}\Riemannzeta@{1-2r}\Riemannzeta@{s+2r}+\sum_{n=1}^{\infty}\frac{1}{n^{s}}\int_{n}^{\infty}\frac{\perBernoulliB{2k+1}@{x}}{x^{2k+2}}\diff{x},}
    0 references
    DLMF id
    DLMF:25.16.E6
    0 references
    Symbols used
    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.m2adec
    0 references
    Q12169
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulersumH@{\NVar{s}}}
    xml-id
    C25.S16.SS2.p1.m1aadec
    0 references
    Riemann zeta function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemannzeta@{\NVar{s}}}
    xml-id
    C25.S2.E1.m2aadec
    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.m1adec
    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.m3adec
    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.m1adec
    0 references
    Q12150
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
    xml-id
    C25.S1.XMD1.m1dec
    0 references
    Q12148
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}
    xml-id
    C25.S1.XMD3.m1adec
    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.m1ddec
    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.m1adec
    0 references
     
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