DLMF:10.22.E31 (Q3405)

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DLMF:10.22.E31
No description defined

    Statements

    Defining formula
    ∫ 0 x J μ ⁡ ( t ) ⁢ J ν ⁡ ( x - t ) ⁢ d t = 2 ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ J μ + ν + 2 ⁢ k + 1 ⁡ ( x ) , superscript subscript 0 𝑥 Bessel-J 𝜇 𝑡 Bessel-J 𝜈 𝑥 𝑡 𝑡 2 superscript subscript 𝑘 0 superscript 1 𝑘 Bessel-J 𝜇 𝜈 2 𝑘 1 𝑥 {\displaystyle{\displaystyle\int_{0}^{x}J_{\mu}\left(t\right)J_{\nu}\left(x-t% \right)\mathrm{d}t=2\sum_{k=0}^{\infty}(-1)^{k}J_{\mu+\nu+2k+1}\left(x\right),}}
    0 references
    DLMF id
    DLMF:10.22.E31
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    constraint
    ℜ ⁡ μ > - 1 , ℜ ⁡ ν > - 1 formulae-sequence 𝜇 1 𝜈 1 {\displaystyle{\displaystyle\Re\mu>-1,\Re\nu>-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.m2awdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aaddec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aaddec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1apdec
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    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1gdec
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    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1idec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1sdec
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