DLMF:10.17.E7 (Q3176): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
Defining formula:

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

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1addec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1edec

Latest revision as of 15:30, 2 January 2020

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DLMF:10.17.E7
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    Statements

    z 1 2 = exp ( 1 2 ln | z | + 1 2 i ph z ) . superscript 𝑧 1 2 1 2 𝑧 1 2 𝑖 phase 𝑧 {\displaystyle{\displaystyle z^{\frac{1}{2}}=\exp\left(\tfrac{1}{2}\ln|z|+% \tfrac{1}{2}i\operatorname{ph}z\right).}}
    0 references
    DLMF:10.17.E7
    0 references
    exp z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    C4.S2.E19.m2adec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2abdec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2adec
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    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1addec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1edec
    0 references