DLMF:4.45.E15 (Q2024): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
test:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1adec

Revision as of 18:27, 1 January 2020

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DLMF:4.45.E15
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    Statements

    test
    ln ⁡ z = ln ⁡ | z | + i ⁢ ph ⁡ z , 𝑧 𝑧 𝑖 phase 𝑧 {\displaystyle{\displaystyle\ln z=\ln|z|+i\operatorname{ph}z,}}
    0 references
    DLMF id
    DLMF:4.45.E15
    0 references
    constraint
    - π ≤ ph ⁡ z ≤ π 𝜋 phase 𝑧 𝜋 {\displaystyle{\displaystyle-\pi\leq\operatorname{ph}z\leq\pi}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
     
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