DLMF:7.8.E5 (Q2391)

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DLMF:7.8.E5
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    Statements

    Defining formula
    x 2 2 ⁢ x 2 + 1 ≤ x 2 ⁢ ( 2 ⁢ x 2 + 5 ) 4 ⁢ x 4 + 12 ⁢ x 2 + 3 ≤ x ⁢ 𝖬 ⁡ ( x ) < 2 ⁢ x 4 + 9 ⁢ x 2 + 4 4 ⁢ x 4 + 20 ⁢ x 2 + 15 < x 2 + 1 2 ⁢ x 2 + 3 , superscript 𝑥 2 2 superscript 𝑥 2 1 superscript 𝑥 2 2 superscript 𝑥 2 5 4 superscript 𝑥 4 12 superscript 𝑥 2 3 𝑥 Mills-ratio 𝑥 2 superscript 𝑥 4 9 superscript 𝑥 2 4 4 superscript 𝑥 4 20 superscript 𝑥 2 15 superscript 𝑥 2 1 2 superscript 𝑥 2 3 {\displaystyle{\displaystyle\frac{x^{2}}{2x^{2}+1}\leq\frac{x^{2}(2x^{2}+5)}{4% x^{4}+12x^{2}+3}\leq x\mathsf{M}\left(x\right)<\frac{2x^{4}+9x^{2}+4}{4x^{4}+2% 0x^{2}+15}<\frac{x^{2}+1}{2x^{2}+3},}}
    0 references
    DLMF id
    DLMF:7.8.E5
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    constraint
    x ≥ 0 𝑥 0 {\displaystyle{\displaystyle x\geq 0}}
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    Symbols used
    Mills’ ratio
    Defining formula
    𝖬 ⁡ ( x ) Mills-ratio 𝑥 {\displaystyle{\displaystyle\mathsf{M}\left(\NVar{x}\right)}}
    xml-id
    C7.S8.E1.m2addec
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    Q11313
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C7.S1.XMD1.m1ddec
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