DLMF:2.7.E31 (Q925): 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 < 0 𝑥 {\displaystyle{\displaystyle 0<x<\infty}}

0<x<\infty
Property / constraint: 0 < x < 0 𝑥 {\displaystyle{\displaystyle 0<x<\infty}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
Defining formula:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2addec
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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11043 / rank
 
Normal rank
Property / Symbols used: Q11043 / qualifier
 
Defining formula:

w 𝑤 {\displaystyle{\displaystyle w}}

w
Property / Symbols used: Q11043 / qualifier
 
xml-id: C2.S7.XMD1.m1cdec

Latest revision as of 17:24, 1 January 2020

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DLMF:2.7.E31
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    Statements

    d 2 w d x 2 = ( x + ln x ) w , derivative 𝑤 𝑥 2 𝑥 𝑥 𝑤 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}x}^{2}}=(x+\ln x% )w,}}
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    DLMF:2.7.E31
    0 references
    0 < x < 0 𝑥 {\displaystyle{\displaystyle 0<x<\infty}}
    0 references
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2addec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aadec
    0 references
    w 𝑤 {\displaystyle{\displaystyle w}}
    C2.S7.XMD1.m1cdec
    0 references