DLMF:10.14.E7 (Q3144)

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DLMF:10.14.E7
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    Statements

    Defining formula
    1 ≤ J ν ⁡ ( ν ⁢ x ) x ν ⁢ J ν ⁡ ( ν ) ≤ e ν ⁢ ( 1 - x ) , 1 Bessel-J 𝜈 𝜈 𝑥 superscript 𝑥 𝜈 Bessel-J 𝜈 𝜈 superscript 𝑒 𝜈 1 𝑥 {\displaystyle{\displaystyle 1\leq\frac{J_{\nu}\left(\nu x\right)}{x^{\nu}J_{% \nu}\left(\nu\right)}\leq e^{\nu(1-x)},}}
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    DLMF id
    DLMF:10.14.E7
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    constraint
    ν ≥ 0 , 0 < x ≤ 1 formulae-sequence 𝜈 0 0 𝑥 1 {\displaystyle{\displaystyle\nu\geq 0,0<x\leq 1}}
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    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2afdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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