DLMF:10.22.E76 (Q3451)

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DLMF:10.22.E76
No description defined

    Statements

    Defining formula
    g ⁢ ( y ) = ∫ 0 ∞ f ⁢ ( x ) ⁢ J ν ⁡ ( x ⁢ y ) ⁢ ( x ⁢ y ) 1 2 ⁢ d x . 𝑔 𝑦 superscript subscript 0 𝑓 𝑥 Bessel-J 𝜈 𝑥 𝑦 superscript 𝑥 𝑦 1 2 𝑥 {\displaystyle{\displaystyle g(y)=\int_{0}^{\infty}f(x)J_{\nu}\left(xy\right)(% xy)^{\frac{1}{2}}\mathrm{d}x.}}
    0 references
    DLMF id
    DLMF:10.22.E76
    0 references
    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.m2abhdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abvdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abvdec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1rdec
    0 references
    Q11472
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C10.S1.XMD5.m1dec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1badec
    0 references
    Q11473
    Defining formula
    f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}
    xml-id
    C10.S22.XMD4.m1dec
    0 references
    Q11474
    Defining formula
    g ⁢ ( y ) 𝑔 𝑦 {\displaystyle{\displaystyle g(y)}}
    xml-id
    C10.S22.XMD5.m1dec
    0 references
     
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