DLMF:4.37.E29 (Q1948): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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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.m2aidec
Property / Symbols used
 
Property / Symbols used: general inverse hyperbolic sine function / rank
 
Normal rank
Property / Symbols used: general inverse hyperbolic sine function / qualifier
 
Defining formula:

Arcsinh z multivalued-hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{Arcsinh}\NVar{z}}}

\Asinh@@{\NVar{z}}
Property / Symbols used: general inverse hyperbolic sine function / qualifier
 
xml-id: C4.S37.E1.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.m1dec
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.m1wdec

Latest revision as of 19:18, 1 January 2020

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DLMF:4.37.E29
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    Statements

    w = Arcsinh z = ( - 1 ) k arcsinh z + k π i , 𝑤 multivalued-hyperbolic-inverse-sine 𝑧 superscript 1 𝑘 hyperbolic-inverse-sine 𝑧 𝑘 𝜋 𝑖 {\displaystyle{\displaystyle w=\operatorname{Arcsinh}z=(-1)^{k}\operatorname{% arcsinh}z+k\pi i,}}
    0 references
    DLMF:4.37.E29
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2agdec
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    arcsinh z hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}
    C4.S37.SS2.p1.m8afdec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aidec
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    Arcsinh z multivalued-hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{Arcsinh}\NVar{z}}}
    C4.S37.E1.m2abdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C4.S1.XMD1.m1dec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1wdec
    0 references