DLMF:4.37.E30 (Q1949): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11246 / rank
 
Normal rank
Property / Symbols used: Q11246 / qualifier
 
Defining formula:

arccosh ⁡ z hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}

\acosh@@{\NVar{z}}
Property / Symbols used: Q11246 / qualifier
 
xml-id: C4.S37.SS2.p1.m9ahdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

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: general inverse hyperbolic cosine function / rank
 
Normal rank
Property / Symbols used: general inverse hyperbolic cosine function / qualifier
 
Defining formula:

Arccosh ⁡ z multivalued-hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{Arccosh}\NVar{z}}}

\Acosh@@{\NVar{z}}
Property / Symbols used: general inverse hyperbolic cosine function / qualifier
 
xml-id: C4.S37.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11219 / rank
 
Normal rank
Property / Symbols used: Q11219 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11219 / qualifier
 
xml-id: C4.S1.XMD1.m1adec
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.m1xdec

Latest revision as of 19:18, 1 January 2020

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DLMF:4.37.E30
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    Statements

    Defining formula
    w = Arccosh ⁡ z = ± arccosh ⁡ z + 2 ⁢ k ⁢ π ⁢ i , 𝑤 multivalued-hyperbolic-inverse-cosine 𝑧 plus-or-minus hyperbolic-inverse-cosine 𝑧 2 𝑘 𝜋 𝑖 {\displaystyle{\displaystyle w=\operatorname{Arccosh}z=\pm\operatorname{% arccosh}z+2k\pi i,}}
    0 references
    DLMF id
    DLMF:4.37.E30
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
    Q11246
    Defining formula
    arccosh ⁡ z hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m9ahdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ajdec
    0 references
    general inverse hyperbolic cosine function
    Defining formula
    Arccosh ⁡ z multivalued-hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{Arccosh}\NVar{z}}}
    xml-id
    C4.S37.E2.m2abdec
    0 references
    Q11219
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C4.S1.XMD1.m1adec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1xdec
    0 references
     
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