DLMF:4.2.E30 (Q1526)

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DLMF:4.2.E30
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    Statements

    Defining formula
    ph ⁡ ( z a ) = ( ℜ ⁡ a ) ⁢ ph ⁡ z + ( ℑ ⁡ a ) ⁢ ln ⁡ | z | , phase superscript 𝑧 𝑎 𝑎 phase 𝑧 𝑎 𝑧 {\displaystyle{\displaystyle\operatorname{ph}\left(z^{a}\right)=(\Re a)% \operatorname{ph}z+(\Im a)\ln|z|,}}
    0 references
    DLMF id
    DLMF:4.2.E30
    0 references
    Symbols used
    Q10901
    Defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2abdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2amdec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1addec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
    Q11221
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1fdec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1wdec
    0 references
     
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