DLMF:4.26.E17 (Q1833): 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: arccosecant function / rank
 
Normal rank
Property / Symbols used: arccosecant function / qualifier
 
Defining formula:

arccsc z 𝑧 {\displaystyle{\displaystyle\operatorname{arccsc}\NVar{z}}}

\acsc@@{\NVar{z}}
Property / Symbols used: arccosecant function / qualifier
 
xml-id: C4.S23.E7.m2adec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

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.m2addec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1kdec

Latest revision as of 18:43, 1 January 2020

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DLMF:4.26.E17
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    Statements

    arccsc x d x = x arccsc x + ln ( x + ( x 2 - 1 ) 1 / 2 ) , 𝑥 𝑥 𝑥 𝑥 𝑥 superscript superscript 𝑥 2 1 1 2 {\displaystyle{\displaystyle\int\operatorname{arccsc}x\mathrm{d}x=x% \operatorname{arccsc}x+\ln\left(x+(x^{2}-1)^{1/2}\right),}}
    0 references
    DLMF:4.26.E17
    0 references
    1 < x < 1 𝑥 {\displaystyle{\displaystyle 1<x<\infty}}
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1apdec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3apdec
    0 references
    arccsc z 𝑧 {\displaystyle{\displaystyle\operatorname{arccsc}\NVar{z}}}
    C4.S23.E7.m2adec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2addec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1kdec
    0 references