DLMF:2.7.E25 (Q919)

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DLMF:2.7.E25
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    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
     
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