DLMF:4.8.E4 (Q1595): Difference between revisions

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Property / constraint
 

- π ph z 1 - ph z 2 π 𝜋 phase subscript 𝑧 1 phase subscript 𝑧 2 𝜋 {\displaystyle{\displaystyle-\pi\leq\operatorname{ph}z_{1}-\operatorname{ph}z_% {2}\leq\pi}}

-\pi\leq\phase@@{z_{1}}-\phase@@{z_{2}}\leq\pi
Property / constraint: - π ph z 1 - ph z 2 π 𝜋 phase subscript 𝑧 1 phase subscript 𝑧 2 𝜋 {\displaystyle{\displaystyle-\pi\leq\operatorname{ph}z_{1}-\operatorname{ph}z_% {2}\leq\pi}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aadec
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.m2aadec
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.m1aadec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1cdec

Latest revision as of 18:11, 1 January 2020

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DLMF:4.8.E4
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    Statements

    ln z 1 z 2 = ln z 1 - ln z 2 , subscript 𝑧 1 subscript 𝑧 2 subscript 𝑧 1 subscript 𝑧 2 {\displaystyle{\displaystyle\ln\frac{z_{1}}{z_{2}}=\ln z_{1}-\ln z_{2},}}
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    DLMF:4.8.E4
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    - π ph z 1 - ph z 2 π 𝜋 phase subscript 𝑧 1 phase subscript 𝑧 2 𝜋 {\displaystyle{\displaystyle-\pi\leq\operatorname{ph}z_{1}-\operatorname{ph}z_% {2}\leq\pi}}
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aadec
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    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1cdec
    0 references