DLMF:4.37.E31 (Q1950): Difference between revisions

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Property / constraint
 

z ± 1 𝑧 plus-or-minus 1 {\displaystyle{\displaystyle z\neq\pm 1}}

z\neq\pm 1
Property / constraint: z ± 1 𝑧 plus-or-minus 1 {\displaystyle{\displaystyle z\neq\pm 1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aidec
Property / Symbols used
 
Property / Symbols used: Q11248 / rank
 
Normal rank
Property / Symbols used: Q11248 / qualifier
 
test:

arctanh z hyperbolic-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}

\atanh@@{\NVar{z}}
Property / Symbols used: Q11248 / qualifier
 
xml-id: C4.S37.SS2.p1.m10aedec
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.m2akdec
Property / Symbols used
 
Property / Symbols used: general inverse hyperbolic tangent function / rank
 
Normal rank
Property / Symbols used: general inverse hyperbolic tangent function / qualifier
 
test:

Arctanh z multivalued-hyperbolic-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{Arctanh}\NVar{z}}}

\Atanh@@{\NVar{z}}
Property / Symbols used: general inverse hyperbolic tangent function / qualifier
 
xml-id: C4.S37.E3.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11219 / rank
 
Normal rank
Property / Symbols used: Q11219 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11219 / qualifier
 
xml-id: C4.S1.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1ydec

Latest revision as of 18:18, 1 January 2020

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DLMF:4.37.E31
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    Statements

    w = Arctanh z = arctanh z + k π i , 𝑤 multivalued-hyperbolic-inverse-tangent 𝑧 hyperbolic-inverse-tangent 𝑧 𝑘 𝜋 𝑖 {\displaystyle{\displaystyle w=\operatorname{Arctanh}z=\operatorname{arctanh}z% +k\pi i,}}
    0 references
    0 references
    z ± 1 𝑧 plus-or-minus 1 {\displaystyle{\displaystyle z\neq\pm 1}}
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aidec
    0 references
    arctanh z hyperbolic-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}
    C4.S37.SS2.p1.m10aedec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2akdec
    0 references
    Arctanh z multivalued-hyperbolic-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{Arctanh}\NVar{z}}}
    C4.S37.E3.m2abdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C4.S1.XMD1.m1bdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1ydec
    0 references