DLMF:10.14.E5 (Q3142)

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DLMF:10.14.E5
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    Statements

    test
    | J ν ⁡ ( ν ⁢ x ) | ≤ x ν ⁢ exp ⁡ ( ν ⁢ ( 1 - x 2 ) 1 2 ) ( 1 + ( 1 - x 2 ) 1 2 ) ν , Bessel-J 𝜈 𝜈 𝑥 superscript 𝑥 𝜈 𝜈 superscript 1 superscript 𝑥 2 1 2 superscript 1 superscript 1 superscript 𝑥 2 1 2 𝜈 {\displaystyle{\displaystyle|J_{\nu}\left(\nu x\right)|\leq\frac{x^{\nu}\exp% \left(\nu(1-x^{2})^{\frac{1}{2}}\right)}{\left(1+(1-x^{2})^{\frac{1}{2}}\right% )^{\nu}},}}
    0 references
    DLMF id
    DLMF:10.14.E5
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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
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2addec
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    exponential function
    test
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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