DLMF:10.14.E6 (Q3143)

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DLMF:10.14.E6
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    Statements

    Defining formula
    | J ν ′ ⁡ ( ν ⁢ x ) | ≤ ( 1 + x 2 ) 1 4 x ⁢ ( 2 ⁢ π ⁢ ν ) 1 2 ⁢ x ν ⁢ exp ⁡ ( ν ⁢ ( 1 - x 2 ) 1 2 ) ( 1 + ( 1 - x 2 ) 1 2 ) ν , diffop Bessel-J 𝜈 1 𝜈 𝑥 superscript 1 superscript 𝑥 2 1 4 𝑥 superscript 2 𝜋 𝜈 1 2 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{(1+x^{2})^{% \frac{1}{4}}}{x(2\pi\nu)^{\frac{1}{2}}}\frac{x^{\nu}\exp\left(\nu(1-x^{2})^{% \frac{1}{2}}\right)}{\left(1+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}},}}
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    DLMF id
    DLMF:10.14.E6
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    constraint
    ν > 0 , 0 < x ≤ 1 formulae-sequence 𝜈 0 0 𝑥 1 {\displaystyle{\displaystyle\nu>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.m2aedec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2aadec
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    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1bdec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1ddec
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