DLMF:5.5.E4 (Q2062)

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DLMF:5.5.E4
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    Statements

    Defining formula
    ψ ⁡ ( z ) - ψ ⁡ ( 1 - z ) = - π / tan ⁡ ( π ⁢ z ) , digamma 𝑧 digamma 1 𝑧 𝜋 𝜋 𝑧 {\displaystyle{\displaystyle\psi\left(z\right)-\psi\left(1-z\right)=-\pi/\tan% \left(\pi z\right),}}
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    DLMF id
    DLMF:5.5.E4
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    constraint
    z ≠ 0 , ± 1 , … 𝑧 0 plus-or-minus 1 … {\displaystyle{\displaystyle z\neq 0,\pm 1,\dots}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2aadec
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    tangent function
    Defining formula
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2adec
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