DLMF:5.16.E2 (Q2179): Difference between revisions

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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.m2aadec

Revision as of 00:08, 2 January 2020

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DLMF:5.16.E2
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    Statements

    test
    ∑ k = 1 ∞ 1 k ⁢ ψ ′ ⁡ ( k + 1 ) = ζ ⁡ ( 3 ) = - 1 2 ⁢ ψ ′′ ⁡ ( 1 ) . superscript subscript 𝑘 1 1 𝑘 diffop digamma 1 𝑘 1 Riemann-zeta 3 1 2 diffop digamma 2 1 {\displaystyle{\displaystyle\sum_{k=1}^{\infty}\frac{1}{k}\psi'\left(k+1\right% )=\zeta\left(3\right)=-\frac{1}{2}\psi''\left(1\right).}}
    0 references
    DLMF id
    DLMF:5.16.E2
    0 references
    Symbols used
    Riemann zeta function
    test
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2adec
    0 references
    psi (or digamma) function
    test
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2aadec
    0 references
     
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