DLMF:2.5.E13 (Q789)

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DLMF:2.5.E13
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    Statements

    Defining formula
    b n = - a n ⁢ ( ln ⁡ 2 + 1 2 ⁢ ψ ⁡ ( ν + 1 2 ⁢ n ) + ψ ⁡ ( 1 - 1 2 ⁢ n ) + 1 2 ⁢ ψ ⁡ ( 1 + ν - 1 2 ⁢ n ) - ψ ⁡ ( n ) ) , subscript 𝑏 𝑛 subscript 𝑎 𝑛 2 1 2 digamma 𝜈 1 2 𝑛 digamma 1 1 2 𝑛 1 2 digamma 1 𝜈 1 2 𝑛 digamma 𝑛 {\displaystyle{\displaystyle b_{n}=-a_{n}\left(\ln 2+\tfrac{1}{2}\psi\left(\nu% +\tfrac{1}{2}n\right)+\psi\left(1-\tfrac{1}{2}n\right)+\tfrac{1}{2}\psi\left(1% +\nu-\tfrac{1}{2}n\right)-\psi\left(n\right)\right),}}
    0 references
    DLMF id
    DLMF:2.5.E13
    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
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
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    Q11000
    Defining formula
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C2.S5.XMD11.m1bdec
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    Q11001
    Defining formula
    b n subscript 𝑏 𝑛 {\displaystyle{\displaystyle b_{n}}}
    xml-id
    C2.S5.XMD12.m1adec
    0 references
     
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