DLMF:28.19.E1 (Q8329)

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DLMF:28.19.E1
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    Statements

    Defining formula
    f ⁢ ( z + π ) = e i ⁢ ν ⁢ π ⁢ f ⁢ ( z ) . 𝑓 𝑧 𝜋 superscript 𝑒 imaginary-unit 𝜈 𝜋 𝑓 𝑧 {\displaystyle{\displaystyle f(z+\pi)=e^{\mathrm{i}\nu\pi}f(z).}}
    0 references
    DLMF id
    DLMF:28.19.E1
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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.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1dec
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    Q12278
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C28.S1.XMD7.m1dec
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    function (locally)
    Defining formula
    f ⁢ ( z ) 𝑓 𝑧 {\displaystyle{\displaystyle f(z)}}
    xml-id
    C28.S19.XMD1.m1dec
    0 references
     
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