DLMF:10.14.E4 (Q3141)

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DLMF:10.14.E4
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    Statements

    test
    | J ν ⁡ ( z ) | ≤ | 1 2 ⁢ z | ν ⁢ e | ℑ ⁡ z | Γ ⁡ ( ν + 1 ) , Bessel-J 𝜈 𝑧 superscript 1 2 𝑧 𝜈 superscript 𝑒 𝑧 Euler-Gamma 𝜈 1 {\displaystyle{\displaystyle|J_{\nu}\left(z\right)|\leq\frac{|\tfrac{1}{2}z|^{% \nu}e^{|\Im z|}}{\Gamma\left(\nu+1\right)},}}
    0 references
    DLMF id
    DLMF:10.14.E4
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    constraint
    ν ≥ - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\nu\geq-\frac{1}{2}}}
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    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2acdec
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    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
     
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