DLMF:5.7.E4 (Q2080): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Riemann zeta function / rank
 
Normal rank
Property / Symbols used: Riemann zeta function / qualifier
 
test:

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.m2abdec
Property / Symbols used
 
Property / Symbols used: psi (or digamma) function / rank
 
Normal rank
Property / Symbols used: psi (or digamma) function / qualifier
 
test:

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: Q11279 / rank
 
Normal rank
Property / Symbols used: Q11279 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11279 / qualifier
 
xml-id: C5.S1.XMD4.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11273 / rank
 
Normal rank
Property / Symbols used: Q11273 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11273 / qualifier
 
xml-id: C5.S1.XMD7.m1bdec

Latest revision as of 18:33, 1 January 2020

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DLMF:5.7.E4
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    Statements

    ψ ( 1 + z ) = - γ + k = 2 ( - 1 ) k ζ ( k ) z k - 1 , digamma 1 𝑧 superscript subscript 𝑘 2 superscript 1 𝑘 Riemann-zeta 𝑘 superscript 𝑧 𝑘 1 {\displaystyle{\displaystyle\psi\left(1+z\right)=-\gamma+\sum_{k=2}^{\infty}(-% 1)^{k}\zeta\left(k\right)z^{k-1},}}
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    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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    γ {\displaystyle{\displaystyle\gamma}}
    C5.S2.E3.m2abdec
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    ζ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    C25.S2.E1.m2abdec
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    ψ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    C5.S2.E2.m2adec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C5.S1.XMD4.m1cdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C5.S1.XMD7.m1bdec
    0 references