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DLMF:7.8.E2 - MaRDI portal

DLMF:7.8.E2 (Q3086)

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DLMF:7.8.E2
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    Statements

    DLMF defining formula
    1 x + x 2 + 2 < 𝖬 ⁡ ( x ) ≤ 1 x + x 2 + ( 4 / π ) , 1 𝑥 superscript 𝑥 2 2 Mills-ratio 𝑥 1 𝑥 superscript 𝑥 2 4 𝜋 {\displaystyle{\displaystyle\frac{1}{x+\sqrt{x^{2}+2}}<\mathsf{M}\left(x\right% )\leq\frac{1}{x+\sqrt{x^{2}+(4/\pi)}},}}
    0 references
    constraint
    x ≥ 0 𝑥 0 {\displaystyle{\displaystyle x\geq 0}}
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    Symbols used
    Mills’ ratio
    DLMF defining formula
    𝖬 ⁡ ( x ) Mills-ratio 𝑥 {\displaystyle{\displaystyle\mathsf{M}\left(\NVar{x}\right)}}
    xml-id
    C7.S8.E1.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C7.S1.XMD1.m1adec
    0 references

    Identifiers

     
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