DLMF:4.38.E3 (Q1953): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(3 intermediate revisions by the same user not shown)
Property / constraint
 

| z | > 1 𝑧 1 {\displaystyle{\displaystyle|z|>1}}

|z|>1
Property / constraint: | z | > 1 𝑧 1 {\displaystyle{\displaystyle|z|>1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q11246 / rank
 
Normal rank
Property / Symbols used: Q11246 / qualifier
 
test:

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.m9adec
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.m2aadec
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.m1bdec

Latest revision as of 18:19, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:4.38.E3
No description defined

    Statements

    arccosh z = ln ( 2 z ) - 1 2 1 2 z 2 - 1 3 2 4 1 4 z 4 - 1 3 5 2 4 6 1 6 z 6 - , hyperbolic-inverse-cosine 𝑧 2 𝑧 1 2 1 2 superscript 𝑧 2 1 3 2 4 1 4 superscript 𝑧 4 1 3 5 2 4 6 1 6 superscript 𝑧 6 {\displaystyle{\displaystyle\operatorname{arccosh}z=\ln\left(2z\right)-\frac{1% }{2}\frac{1}{2z^{2}}-\frac{1\cdot 3}{2\cdot 4}\frac{1}{4z^{4}}-\frac{1\cdot 3% \cdot 5}{2\cdot 4\cdot 6}\frac{1}{6z^{6}}-\cdots,}}
    0 references
    0 references
    | z | > 1 𝑧 1 {\displaystyle{\displaystyle|z|>1}}
    0 references
    arccosh z hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}
    C4.S37.SS2.p1.m9adec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1bdec
    0 references