DLMF:10.22.E37 (Q3411)

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DLMF:10.22.E37
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    Statements

    Defining formula
    ∫ 0 1 t ⁢ J ν ⁡ ( j ν , ℓ ⁢ t ) ⁢ J ν ⁡ ( j ν , m ⁢ t ) ⁢ d t = 1 2 ⁢ ( J ν ′ ⁡ ( j ν , ℓ ) ) 2 ⁢ δ ℓ , m , superscript subscript 0 1 𝑡 Bessel-J 𝜈 subscript 𝑗 𝜈 ℓ 𝑡 Bessel-J 𝜈 subscript 𝑗 𝜈 𝑚 𝑡 𝑡 1 2 superscript diffop Bessel-J 𝜈 1 subscript 𝑗 𝜈 ℓ 2 Kronecker ℓ 𝑚 {\displaystyle{\displaystyle\int_{0}^{1}tJ_{\nu}\left(j_{\nu,\ell}t\right)J_{% \nu}\left(j_{\nu,m}t\right)\mathrm{d}t=\tfrac{1}{2}\left(J_{\nu}'\left(j_{\nu,% \ell}\right)\right)^{2}\delta_{\ell,m},}}
    0 references
    DLMF id
    DLMF:10.22.E37
    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.m2aacdec
    0 references
    Q10768
    Defining formula
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aajdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aajdec
    0 references
    Q11438
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C10.S1.XMD1.m1dec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1ydec
    0 references
     
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