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DLMF:5.15.E2 - MaRDI portal

DLMF:5.15.E2 (Q2869)

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DLMF:5.15.E2
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    Statements

    DLMF defining formula
    ψ ( n ) ⁡ ( 1 ) = ( - 1 ) n + 1 ⁢ n ! ⁢ ζ ⁡ ( n + 1 ) , polygamma 𝑛 1 superscript 1 𝑛 1 𝑛 Riemann-zeta 𝑛 1 {\displaystyle{\displaystyle\psi^{(n)}\left(1\right)=(-1)^{n+1}n!\zeta\left(n+% 1\right),}}
    0 references
    Symbols used
    Riemann zeta function
    DLMF defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2adec
    0 references
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    polygamma functions
    DLMF defining formula
    ψ ( n ) ⁡ ( z ) polygamma 𝑛 𝑧 {\displaystyle{\displaystyle\psi^{(\NVar{n})}\left(\NVar{z}\right)}}
    xml-id
    C5.S15.m1adec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C5.S1.XMD3.m1dec
    0 references

    Identifiers

     
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