DLMF:4.40.E15 (Q1987): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
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Property / constraint
 

0 < x < 1 0 𝑥 1 {\displaystyle{\displaystyle 0<x<1}}

0<x<1
Property / constraint: 0 < x < 1 0 𝑥 1 {\displaystyle{\displaystyle 0<x<1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1andec
Property / Symbols used
 
Property / Symbols used: inverse hyperbolic secant function / rank
 
Normal rank
Property / Symbols used: inverse hyperbolic secant function / qualifier
 
Defining formula:

arcsech z hyperbolic-inverse-secant 𝑧 {\displaystyle{\displaystyle\operatorname{arcsech}\NVar{z}}}

\asech@@{\NVar{z}}
Property / Symbols used: inverse hyperbolic secant function / qualifier
 
xml-id: C4.S37.E8.m2adec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3andec
Property / Symbols used
 
Property / Symbols used: Q11242 / rank
 
Normal rank
Property / Symbols used: Q11242 / qualifier
 
Defining formula:

arcsin z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}

\asin@@{\NVar{z}}
Property / Symbols used: Q11242 / qualifier
 
xml-id: C4.S23.SS2.p1.m5adec
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.m1ndec

Latest revision as of 19:23, 1 January 2020

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DLMF:4.40.E15
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    Statements

    arcsech x d x = x arcsech x + arcsin x , hyperbolic-inverse-secant 𝑥 𝑥 𝑥 hyperbolic-inverse-secant 𝑥 𝑥 {\displaystyle{\displaystyle\int\operatorname{arcsech}x\mathrm{d}x=x% \operatorname{arcsech}x+\operatorname{arcsin}x,}}
    0 references
    DLMF:4.40.E15
    0 references
    0 < x < 1 0 𝑥 1 {\displaystyle{\displaystyle 0<x<1}}
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1andec
    0 references
    arcsech z hyperbolic-inverse-secant 𝑧 {\displaystyle{\displaystyle\operatorname{arcsech}\NVar{z}}}
    C4.S37.E8.m2adec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3andec
    0 references
    arcsin z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}
    C4.S23.SS2.p1.m5adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1ndec
    0 references