DLMF:4.40.E16 (Q1988): Difference between revisions

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Property / constraint
 

1 < x < 1 𝑥 {\displaystyle{\displaystyle 1<x<\infty}}

1<x<\infty
Property / constraint: 1 < x < 1 𝑥 {\displaystyle{\displaystyle 1<x<\infty}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aodec
Property / Symbols used
 
Property / Symbols used: inverse hyperbolic cotangent function / rank
 
Normal rank
Property / Symbols used: inverse hyperbolic cotangent function / qualifier
 
test:

arccoth z hyperbolic-inverse-cotangent 𝑧 {\displaystyle{\displaystyle\operatorname{arccoth}\NVar{z}}}

\acoth@@{\NVar{z}}
Property / Symbols used: inverse hyperbolic cotangent function / qualifier
 
xml-id: C4.S37.E9.m2adec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aodec
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.m2aedec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1odec

Latest revision as of 18:23, 1 January 2020

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DLMF:4.40.E16
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    Statements

    arccoth x d x = x arccoth x + 1 2 ln ( x 2 - 1 ) , hyperbolic-inverse-cotangent 𝑥 𝑥 𝑥 hyperbolic-inverse-cotangent 𝑥 1 2 superscript 𝑥 2 1 {\displaystyle{\displaystyle\int\operatorname{arccoth}x\mathrm{d}x=x% \operatorname{arccoth}x+\tfrac{1}{2}\ln\left(x^{2}-1\right),}}
    0 references
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    1 < x < 1 𝑥 {\displaystyle{\displaystyle 1<x<\infty}}
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aodec
    0 references
    arccoth z hyperbolic-inverse-cotangent 𝑧 {\displaystyle{\displaystyle\operatorname{arccoth}\NVar{z}}}
    C4.S37.E9.m2adec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aodec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aedec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1odec
    0 references