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DLMF:7.8.E6 - MaRDI portal

DLMF:7.8.E6 (Q3090)

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DLMF:7.8.E6
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    Statements

    DLMF defining formula
    ∫ 0 x e a ⁢ t 2 ⁢ d t < 1 3 ⁢ a ⁢ x ⁢ ( 2 ⁢ e a ⁢ x 2 + a ⁢ x 2 - 2 ) , superscript subscript 0 𝑥 superscript 𝑒 𝑎 superscript 𝑡 2 𝑡 1 3 𝑎 𝑥 2 superscript 𝑒 𝑎 superscript 𝑥 2 𝑎 superscript 𝑥 2 2 {\displaystyle{\displaystyle\int_{0}^{x}e^{at^{2}}\mathrm{d}t<\frac{1}{3ax}% \left(2e^{ax^{2}}+ax^{2}-2\right),}}
    0 references
    constraint
    a , x > 0 𝑎 𝑥 0 {\displaystyle{\displaystyle a,x>0}}
    0 references
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C7.S1.XMD1.m1edec
    0 references
     
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