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DLMF:4.2.E28 - MaRDI portal

DLMF:4.2.E28 (Q1567)

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DLMF:4.2.E28
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    Statements

    DLMF defining formula
    z a = exp ⁡ ( a ⁢ ln ⁡ z ) . superscript 𝑧 𝑎 𝑎 𝑧 {\displaystyle{\displaystyle z^{a}=\exp\left(a\ln z\right).}}
    0 references
    Symbols used
    exponential function
    DLMF defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2ahdec
    0 references
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aldec
    0 references
    real or complex constant
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1ddec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1udec
    0 references

    Identifiers

     
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