DLMF:5.4.E19 (Q2057)

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DLMF:5.4.E19
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    Statements

    Defining formula
    ψ ⁡ ( p q ) = - γ - ln ⁡ q - π 2 ⁢ cot ⁡ ( π ⁢ p q ) + 1 2 ⁢ ∑ k = 1 q - 1 cos ⁡ ( 2 ⁢ π ⁢ k ⁢ p q ) ⁢ ln ⁡ ( 2 - 2 ⁢ cos ⁡ ( 2 ⁢ π ⁢ k q ) ) . digamma 𝑝 𝑞 𝑞 𝜋 2 𝜋 𝑝 𝑞 1 2 superscript subscript 𝑘 1 𝑞 1 2 𝜋 𝑘 𝑝 𝑞 2 2 2 𝜋 𝑘 𝑞 {\displaystyle{\displaystyle\psi\left(\frac{p}{q}\right)=-\gamma-\ln q-\frac{% \pi}{2}\cot\left(\frac{\pi p}{q}\right)+\frac{1}{2}\sum_{k=1}^{q-1}\cos\left(% \frac{2\pi kp}{q}\right)\ln\left(2-2\cos\left(\frac{2\pi k}{q}\right)\right).}}
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    DLMF id
    DLMF:5.4.E19
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    Symbols used
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2aedec
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