DLMF:4.23.E27 (Q1779): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
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.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q10777 / rank
 
Normal rank
Property / Symbols used: Q10777 / qualifier
 
Defining formula:

( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}

(\NVar{a},\NVar{b})
Property / Symbols used: Q10777 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r29.m6acdec
Property / Symbols used
 
Property / Symbols used: Q10824 / rank
 
Normal rank
Property / Symbols used: Q10824 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\cup}}

\cup
Property / Symbols used: Q10824 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r28.m2addec
Property / Symbols used
 
Property / Symbols used: Q11222 / rank
 
Normal rank
Property / Symbols used: Q11222 / qualifier
 
Defining formula:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11222 / qualifier
 
xml-id: C4.S1.XMD7.m1dec

Latest revision as of 18:34, 1 January 2020

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DLMF:4.23.E27
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    Statements

    arctan ( i y ) = ± 1 2 π + i 2 ln ( y + 1 y - 1 ) , 𝑖 𝑦 plus-or-minus 1 2 𝜋 𝑖 2 𝑦 1 𝑦 1 {\displaystyle{\displaystyle\operatorname{arctan}\left(iy\right)=\pm\frac{1}{2% }\pi+\frac{i}{2}\ln\left(\frac{y+1}{y-1}\right),}}
    0 references
    DLMF:4.23.E27
    0 references
    y ( - , - 1 ) ( 1 , ) 𝑦 1 1 {\displaystyle{\displaystyle y\in(-\infty,-1)\cup(1,\infty)}}
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aidec
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    {\displaystyle{\displaystyle\in}}
    introduction.Sx4.p1.t1.r10.m2ahdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aldec
    0 references
    arctan z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    C4.S23.SS2.p1.m7aedec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2ahdec
    0 references
    ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    introduction.Sx4.p1.t1.r29.m6acdec
    0 references
    {\displaystyle{\displaystyle\cup}}
    introduction.Sx4.p1.t1.r28.m2addec
    0 references
    y 𝑦 {\displaystyle{\displaystyle y}}
    C4.S1.XMD7.m1dec
    0 references