DLMF:10.22.E55 (Q3429)

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DLMF:10.22.E55
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    Statements

    Defining formula
    ∫ 0 ∞ t - 1 ⁢ J ν + 2 ⁢ ℓ + 1 ⁡ ( t ) ⁢ J ν + 2 ⁢ m + 1 ⁡ ( t ) ⁢ d t = δ ℓ , m 2 ⁢ ( 2 ⁢ ℓ + ν + 1 ) , superscript subscript 0 superscript 𝑡 1 Bessel-J 𝜈 2 ℓ 1 𝑡 Bessel-J 𝜈 2 𝑚 1 𝑡 𝑡 Kronecker ℓ 𝑚 2 2 ℓ 𝜈 1 {\displaystyle{\displaystyle\int_{0}^{\infty}t^{-1}J_{\nu+2\ell+1}\left(t% \right)J_{\nu+2m+1}\left(t\right)\mathrm{d}t=\frac{\delta_{\ell,m}}{2(2\ell+% \nu+1)},}}
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    DLMF id
    DLMF:10.22.E55
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    constraint
    ν + ℓ + m > - 1 𝜈 ℓ 𝑚 1 {\displaystyle{\displaystyle\nu+\ell+m>-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.m2aaodec
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    Q10768
    Defining formula
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5abdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abbdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abbdec
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    Q11438
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C10.S1.XMD1.m1bdec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1andec
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