DLMF:4.23.E25 (Q1777): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2ajdec
Property / Symbols used
 
Property / Symbols used: Q11208 / rank
 
Normal rank
Property / Symbols used: Q11208 / qualifier
 
test:

arccos ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}

\acos@@{\NVar{z}}
Property / Symbols used: Q11208 / qualifier
 
xml-id: C4.S23.SS2.p1.m6agdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

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.m2afdec
Property / Symbols used
 
Property / Symbols used: Q11244 / rank
 
Normal rank
Property / Symbols used: Q11244 / qualifier
 
test:

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

(\NVar{a},\NVar{b}]
Property / Symbols used: Q11244 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r1.m3aadec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1cdec

Latest revision as of 17:33, 1 January 2020

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English
DLMF:4.23.E25
No description defined

    Statements

    test
    arccos ⁡ x = π ∓ i ⁢ ln ⁡ ( ( x 2 - 1 ) 1 / 2 - x ) , 𝑥 minus-or-plus 𝜋 𝑖 superscript superscript 𝑥 2 1 1 2 𝑥 {\displaystyle{\displaystyle\operatorname{arccos}x=\pi\mp i\ln\left((x^{2}-1)^% {1/2}-x\right),}}
    0 references
    DLMF id
    DLMF:4.23.E25
    0 references
    constraint
    x ∈ ( - ∞ , - 1 ] 𝑥 1 {\displaystyle{\displaystyle x\in(-\infty,-1]}}
    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.m2ahdec
    0 references
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2afdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ajdec
    0 references
    Q11208
    test
    arccos ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m6agdec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2afdec
    0 references
    Q11244
    test
    ( a , b ] 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}
    xml-id
    introduction.Sx4.p2.t1.r1.m3aadec
    0 references
    Q11218
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1cdec
    0 references
     
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