DLMF:4.2.E29 (Q1525)

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DLMF:4.2.E29
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    Statements

    Defining formula
    | z a | = | z | ℜ ⁡ a ⁢ exp ⁡ ( - ( ℑ ⁡ a ) ⁢ ph ⁡ z ) , superscript 𝑧 𝑎 superscript 𝑧 𝑎 𝑎 phase 𝑧 {\displaystyle{\displaystyle|z^{a}|=|z|^{\Re a}\exp\left(-(\Im a)\operatorname% {ph}z\right),}}
    0 references
    DLMF id
    DLMF:4.2.E29
    0 references
    Symbols used
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2aidec
    0 references
    Q10901
    Defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2aadec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1acdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
    0 references
    Q11221
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1edec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1vdec
    0 references
     
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