DLMF:4.37.E18 (Q1937): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11247 / rank
 
Normal rank
Property / Symbols used: Q11247 / qualifier
 
test:

arcsinh ⁡ z hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}

\asinh@@{\NVar{z}}
Property / Symbols used: Q11247 / qualifier
 
xml-id: C4.S37.SS2.p1.m8aedec
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.m2addec
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.m2abdec
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.m3adec
Property / Symbols used
 
Property / Symbols used: Q11222 / rank
 
Normal rank
Property / Symbols used: Q11222 / qualifier
 
test:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11222 / qualifier
 
xml-id: C4.S1.XMD7.m1adec

Latest revision as of 18:16, 1 January 2020

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English
DLMF:4.37.E18
No description defined

    Statements

    test
    arcsinh ⁡ ( i ⁢ y ) = - 1 2 ⁢ π ⁢ i ± ln ⁡ ( ( y 2 - 1 ) 1 / 2 - y ) , hyperbolic-inverse-sine 𝑖 𝑦 plus-or-minus 1 2 𝜋 𝑖 superscript superscript 𝑦 2 1 1 2 𝑦 {\displaystyle{\displaystyle\operatorname{arcsinh}\left(iy\right)=-\tfrac{1}{2% }\pi i\pm\ln\left((y^{2}-1)^{1/2}-y\right),}}
    0 references
    DLMF id
    DLMF:4.37.E18
    0 references
    constraint
    y ∈ ( - ∞ , - 1 ] 𝑦 1 {\displaystyle{\displaystyle y\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.m2acdec
    0 references
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2abdec
    0 references
    Q11247
    test
    arcsinh ⁡ z hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m8aedec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
    Q11244
    test
    ( a , b ] 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}
    xml-id
    introduction.Sx4.p2.t1.r1.m3adec
    0 references
    Q11222
    test
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C4.S1.XMD7.m1adec
    0 references
     
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