DLMF:5.15.E3 (Q2172): Difference between revisions

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‎Changed an Item: Add constraint
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Property / Symbols used
 
Property / Symbols used: Q11294 / rank
 
Normal rank
Property / Symbols used: Q11294 / qualifier
 
Defining formula:

ψ ( n ) ⁡ ( z ) polygamma 𝑛 𝑧 {\displaystyle{\displaystyle\psi^{(\NVar{n})}\left(\NVar{z}\right)}}

\polygamma{\NVar{n}}@{\NVar{z}}
Property / Symbols used: Q11294 / qualifier
 
xml-id: C5.S15.m1aadec

Revision as of 01:07, 2 January 2020

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DLMF:5.15.E3
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    Statements

    Defining formula
    ψ ( n ) ⁡ ( 1 2 ) = ( - 1 ) n + 1 ⁢ n ! ⁢ ( 2 n + 1 - 1 ) ⁢ ζ ⁡ ( n + 1 ) , polygamma 𝑛 1 2 superscript 1 𝑛 1 𝑛 superscript 2 𝑛 1 1 Riemann-zeta 𝑛 1 {\displaystyle{\displaystyle\psi^{(n)}\left(\tfrac{1}{2}\right)=(-1)^{n+1}n!(2% ^{n+1}-1)\zeta\left(n+1\right),}}
    0 references
    DLMF id
    DLMF:5.15.E3
    0 references
    Symbols used
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q11294
    Defining formula
    ψ ( n ) ⁡ ( z ) polygamma 𝑛 𝑧 {\displaystyle{\displaystyle\psi^{(\NVar{n})}\left(\NVar{z}\right)}}
    xml-id
    C5.S15.m1aadec
    0 references
     
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