DLMF:10.23.E5 (Q3457)

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DLMF:10.23.E5
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    Statements

    test
    ∑ k = 0 n J k ⁡ ( z ) ⁢ J n - k ⁡ ( z ) + 2 ⁢ ∑ k = 1 ∞ ( - 1 ) k ⁢ J k ⁡ ( z ) ⁢ J n + k ⁡ ( z ) = J n ⁡ ( 2 ⁢ z ) . superscript subscript 𝑘 0 𝑛 Bessel-J 𝑘 𝑧 Bessel-J 𝑛 𝑘 𝑧 2 superscript subscript 𝑘 1 superscript 1 𝑘 Bessel-J 𝑘 𝑧 Bessel-J 𝑛 𝑘 𝑧 Bessel-J 𝑛 2 𝑧 {\displaystyle{\displaystyle\sum_{k=0}^{n}J_{k}\left(z\right)J_{n-k}\left(z% \right)+2\sum_{k=1}^{\infty}(-1)^{k}J_{k}\left(z\right)J_{n+k}\left(z\right)=J% _{n}\left(2z\right).}}
    0 references
    DLMF id
    DLMF:10.23.E5
    0 references
    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.m2acdec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1adec
    0 references
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1ddec
    0 references
     
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