DLMF:15.12.E1 (Q5161): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10816 / rank
 
Normal rank
Property / Symbols used: Q10816 / qualifier
 
Defining formula:

arctan z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

\atan@@{\NVar{z}}
Property / Symbols used: Q10816 / qualifier
 
xml-id: C4.S23.SS2.p1.m7adec
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.m1adec
Property / Symbols used
 
Property / Symbols used: Q11644 / rank
 
Normal rank
Property / Symbols used: Q11644 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11644 / qualifier
 
xml-id: C15.S1.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q11680 / rank
 
Normal rank
Property / Symbols used: Q11680 / qualifier
 
Defining formula:

α ± subscript 𝛼 plus-or-minus {\displaystyle{\displaystyle\alpha_{\pm}}}

\alpha_{\pm}
Property / Symbols used: Q11680 / qualifier
 
xml-id: C15.S12.XMD1.m1dec

Latest revision as of 14:23, 2 January 2020

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DLMF:15.12.E1
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    Statements

    α ± = arctan ( ph z - ph ( 1 - z ) π ln | 1 - z - 1 | ) , subscript 𝛼 plus-or-minus minus-or-plus phase 𝑧 phase 1 𝑧 𝜋 1 superscript 𝑧 1 {\displaystyle{\displaystyle\alpha_{\pm}=\operatorname{arctan}\left(\frac{% \operatorname{ph}z-\operatorname{ph}\left(1-z\right)\mp\pi}{\ln|1-z^{-1}|}% \right),}}
    0 references
    DLMF:15.12.E1
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
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    arctan z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    C4.S23.SS2.p1.m7adec
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    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2adec
    0 references
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C15.S1.XMD3.m1dec
    0 references
    α ± subscript 𝛼 plus-or-minus {\displaystyle{\displaystyle\alpha_{\pm}}}
    C15.S12.XMD1.m1dec
    0 references