DLMF:4.23.E35 (Q1787): Difference between revisions

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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.m1addec
Property / Symbols used
 
Property / Symbols used: DLMF:4.23.E37 / rank
 
Normal rank
Property / Symbols used: DLMF:4.23.E37 / qualifier
 
Defining formula:

α 𝛼 {\displaystyle{\displaystyle\alpha}}

\alpha
Property / Symbols used: DLMF:4.23.E37 / qualifier
 
xml-id: C4.S23.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: DLMF:4.23.E38 / rank
 
Normal rank
Property / Symbols used: DLMF:4.23.E38 / qualifier
 
Defining formula:

β 𝛽 {\displaystyle{\displaystyle\beta}}

\beta
Property / Symbols used: DLMF:4.23.E38 / qualifier
 
xml-id: C4.S23.XMD3.m1adec

Latest revision as of 18:35, 1 January 2020

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DLMF:4.23.E35
No description defined

    Statements

    Defining formula
    arccos ⁡ z = arccos ⁡ β - i ⁢ sign ⁡ ( y ) ⁢ ln ⁡ ( α + ( α 2 - 1 ) 1 / 2 ) , 𝑧 𝛽 imaginary-unit sign 𝑦 𝛼 superscript superscript 𝛼 2 1 1 2 {\displaystyle{\displaystyle\operatorname{arccos}z=\operatorname{arccos}\beta-% \mathrm{i}\operatorname{sign}\left(y\right)\ln\left(\alpha+(\alpha^{2}-1)^{1/2% }\right),}}
    0 references
    DLMF id
    DLMF:4.23.E35
    0 references
    Symbols used
    Q10815
    Defining formula
    [ a , b ] 𝑎 𝑏 {\displaystyle{\displaystyle[\NVar{a},\NVar{b}]}}
    xml-id
    introduction.Sx4.p1.t1.r30.m6aadec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2ajdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aodec
    0 references
    Q11208
    Defining formula
    arccos ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m6aidec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2ajdec
    0 references
    Q11245
    Defining formula
    ∉ {\displaystyle{\displaystyle\notin}}
    xml-id
    introduction.Sx4.p1.t1.r11.m2aadec
    0 references
    Q10777
    Defining formula
    ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p1.t1.r29.m6aedec
    0 references
    Q10897
    Defining formula
    sign ⁡ x sign 𝑥 {\displaystyle{\displaystyle\operatorname{sign}\NVar{x}}}
    xml-id
    introduction.Sx4.p2.t1.r18.m6aadec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1edec
    0 references
    Q11222
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C4.S1.XMD7.m1bdec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1addec
    0 references
    DLMF:4.23.E37
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C4.S23.XMD2.m1adec
    0 references
    DLMF:4.23.E38
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C4.S23.XMD3.m1adec
    0 references
     
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