DLMF:2.7.E25 (Q919): Difference between revisions

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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.m2acdec
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.m1acdec
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.m3acdec
Property / Symbols used
 
Property / Symbols used: total variation / rank
 
Normal rank
Property / Symbols used: total variation / qualifier
 
Defining formula:

𝒱 a , b ⁡ ( f ) variational-operator-on-interval 𝑎 𝑏 𝑓 {\displaystyle{\displaystyle\mathcal{V}_{\NVar{a,b}}\left(\NVar{f}\right)}}

\variation[\NVar{a,b}]@{\NVar{f}}
Property / Symbols used: total variation / qualifier
 
xml-id: C1.S4.E33.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11060 / rank
 
Normal rank
Property / Symbols used: Q11060 / qualifier
 
Defining formula:

( a 1 , a 2 ) subscript 𝑎 1 subscript 𝑎 2 {\displaystyle{\displaystyle(a_{1},a_{2})}}

(a_{1},a_{2})
Property / Symbols used: Q11060 / qualifier
 
xml-id: C2.S7.XMD19.m1adec
Property / Symbols used
 
Property / Symbols used: Q11061 / rank
 
Normal rank
Property / Symbols used: Q11061 / qualifier
 
Defining formula:

F 𝐹 {\displaystyle{\displaystyle F}}

F
Property / Symbols used: Q11061 / qualifier
 
xml-id: C2.S7.XMD23.m1bdec

Latest revision as of 17:23, 1 January 2020

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DLMF:2.7.E25
No description defined

    Statements

    Defining formula
    𝒱 a j , x ⁡ ( F ) = ∫ a j x | ( 1 f 1 / 4 ⁢ ( t ) ⁢ d 2 d t 2 ⁡ ( 1 f 1 / 4 ⁢ ( t ) ) - g ⁢ ( t ) f 1 / 2 ⁢ ( t ) ) ⁢ d t | . variational-operator-on-interval subscript 𝑎 𝑗 𝑥 𝐹 superscript subscript subscript 𝑎 𝑗 𝑥 1 superscript 𝑓 1 4 𝑡 derivative 𝑡 2 1 superscript 𝑓 1 4 𝑡 𝑔 𝑡 superscript 𝑓 1 2 𝑡 𝑡 {\displaystyle{\displaystyle\mathcal{V}_{a_{j},x}\left(F\right)=\int_{a_{j}}^{% x}\left|\left(\frac{1}{f^{1/4}(t)}\frac{{\mathrm{d}}^{2}}{{\mathrm{d}t}^{2}}% \left(\frac{1}{f^{1/4}(t)}\right)-\frac{g(t)}{f^{1/2}(t)}\right)\mathrm{d}t% \right|.}}
    0 references
    DLMF id
    DLMF:2.7.E25
    0 references
    Symbols used
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    total variation
    Defining formula
    𝒱 a , b ⁡ ( f ) variational-operator-on-interval 𝑎 𝑏 𝑓 {\displaystyle{\displaystyle\mathcal{V}_{\NVar{a,b}}\left(\NVar{f}\right)}}
    xml-id
    C1.S4.E33.m2aadec
    0 references
    Q11060
    Defining formula
    ( a 1 , a 2 ) subscript 𝑎 1 subscript 𝑎 2 {\displaystyle{\displaystyle(a_{1},a_{2})}}
    xml-id
    C2.S7.XMD19.m1adec
    0 references
    Q11061
    Defining formula
    F 𝐹 {\displaystyle{\displaystyle F}}
    xml-id
    C2.S7.XMD23.m1bdec
    0 references
     
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