DLMF:25.8.E5 (Q7662): 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 / constraint
 

| z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}

|z|<1
Property / constraint: | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Euler’s constant / rank
 
Normal rank
Property / Symbols used: Euler’s constant / qualifier
 
Defining formula:

γ {\displaystyle{\displaystyle\gamma}}

\EulerConstant
Property / Symbols used: Euler’s constant / qualifier
 
xml-id: C5.S2.E3.m2adec
Property / Symbols used
 
Property / Symbols used: Riemann zeta function / rank
 
Normal rank
Property / Symbols used: Riemann zeta function / qualifier
 
Defining formula:

ζ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}

\Riemannzeta@{\NVar{s}}
Property / Symbols used: Riemann zeta function / qualifier
 
xml-id: C25.S2.E1.m2addec
Property / Symbols used
 
Property / Symbols used: psi (or digamma) function / rank
 
Normal rank
Property / Symbols used: psi (or digamma) function / qualifier
 
Defining formula:

ψ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}

\digamma@{\NVar{z}}
Property / Symbols used: psi (or digamma) function / qualifier
 
xml-id: C5.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q12150 / rank
 
Normal rank
Property / Symbols used: Q12150 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12150 / qualifier
 
xml-id: C25.S1.XMD1.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12156 / rank
 
Normal rank
Property / Symbols used: Q12156 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12156 / qualifier
 
xml-id: C25.S1.XMD8.m1dec

Latest revision as of 13:33, 2 January 2020

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DLMF:25.8.E5
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    Statements

    k = 2 ζ ( k ) z k = - γ z - z ψ ( 1 - z ) , superscript subscript 𝑘 2 Riemann-zeta 𝑘 superscript 𝑧 𝑘 𝑧 𝑧 digamma 1 𝑧 {\displaystyle{\displaystyle\sum_{k=2}^{\infty}\zeta\left(k\right)z^{k}=-% \gamma z-z\psi\left(1-z\right),}}
    0 references
    DLMF:25.8.E5
    0 references
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    γ {\displaystyle{\displaystyle\gamma}}
    C5.S2.E3.m2adec
    0 references
    ζ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    C25.S2.E1.m2addec
    0 references
    ψ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    C5.S2.E2.m2adec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C25.S1.XMD1.m1ddec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C25.S1.XMD8.m1dec
    0 references