DLMF:14.7.E3 (Q4753)

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DLMF:14.7.E3
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    Statements

    Defining formula
    W n - 1 ⁢ ( x ) = ∑ s = 0 n - 1 ( n + s ) ! ⁢ ( ψ ⁡ ( n + 1 ) - ψ ⁡ ( s + 1 ) ) 2 s ⁢ ( n - s ) ! ⁢ ( s ! ) 2 ⁢ ( x - 1 ) s ; subscript 𝑊 𝑛 1 𝑥 superscript subscript 𝑠 0 𝑛 1 𝑛 𝑠 digamma 𝑛 1 digamma 𝑠 1 superscript 2 𝑠 𝑛 𝑠 superscript 𝑠 2 superscript 𝑥 1 𝑠 {\displaystyle{\displaystyle W_{n-1}(x)=\sum_{s=0}^{n-1}\frac{(n+s)!(\psi\left% (n+1\right)-\psi\left(s+1\right))}{2^{s}(n-s)!(s!)^{2}}{(x-1)^{s}};}}
    0 references
    DLMF id
    DLMF:14.7.E3
    0 references
    Symbols used
    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1bdec
    0 references
    Q11602
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1bdec
    0 references
    Q11603
    Defining formula
    W n - 1 ⁢ ( x ) subscript 𝑊 𝑛 1 𝑥 {\displaystyle{\displaystyle W_{n-1}(x)}}
    xml-id
    C14.S7.XMD1.m1adec
    0 references
     
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