DLMF:10.23.E4 (Q3456)

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DLMF:10.23.E4
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    Statements

    test
    ∑ k = 0 2 ⁢ n ( - 1 ) k ⁢ J k ⁡ ( z ) ⁢ J 2 ⁢ n - k ⁡ ( z ) + 2 ⁢ ∑ k = 1 ∞ J k ⁡ ( z ) ⁢ J 2 ⁢ n + k ⁡ ( z ) = 0 , superscript subscript 𝑘 0 2 𝑛 superscript 1 𝑘 Bessel-J 𝑘 𝑧 Bessel-J 2 𝑛 𝑘 𝑧 2 superscript subscript 𝑘 1 Bessel-J 𝑘 𝑧 Bessel-J 2 𝑛 𝑘 𝑧 0 {\displaystyle{\displaystyle\sum_{k=0}^{2n}(-1)^{k}J_{k}\left(z\right)J_{2n-k}% \left(z\right)\\ +2\sum_{k=1}^{\infty}J_{k}\left(z\right)J_{2n+k}\left(z\right)=0,}}
    0 references
    DLMF id
    DLMF:10.23.E4
    0 references
    constraint
    n ≥ 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}}
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    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2abdec
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    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1dec
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