DLMF:5.15.E7 (Q2176)

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DLMF:5.15.E7
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    Statements

    Defining formula
    ψ ( n ) ⁡ ( m ⁢ z ) = 1 m n + 1 ⁢ ∑ k = 0 m - 1 ψ ( n ) ⁡ ( z + k m ) . digamma 𝑛 𝑚 𝑧 1 superscript 𝑚 𝑛 1 superscript subscript 𝑘 0 𝑚 1 digamma 𝑛 𝑧 𝑘 𝑚 {\displaystyle{\displaystyle{\psi^{(n)}}\left(mz\right)=\frac{1}{m^{n+1}}\sum_% {k=0}^{m-1}{\psi^{(n)}}\left(z+\frac{k}{m}\right).}}
    0 references
    DLMF id
    DLMF:5.15.E7
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    Symbols used
    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2addec
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    Q11276
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C5.S1.XMD2.m1dec
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    Q11274
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C5.S1.XMD3.m1edec
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    Q11279
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C5.S1.XMD4.m1bdec
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    Q11273
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1cdec
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