DLMF:10.23.E2 (Q3454)

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DLMF:10.23.E2
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    Statements

    Defining formula
    𝒞 ν ⁡ ( u ± v ) = ∑ k = - ∞ ∞ 𝒞 ν ∓ k ⁡ ( u ) ⁢ J k ⁡ ( v ) , cylinder-function 𝜈 plus-or-minus 𝑢 𝑣 superscript subscript 𝑘 cylinder-function minus-or-plus 𝜈 𝑘 𝑢 Bessel-J 𝑘 𝑣 {\displaystyle{\displaystyle\mathscr{C}_{\nu}\left(u\pm v\right)=\sum_{k=-% \infty}^{\infty}\mathscr{C}_{\nu\mp k}\left(u\right)J_{k}\left(v\right),}}
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    DLMF id
    DLMF:10.23.E2
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    constraint
    | v | < | u | 𝑣 𝑢 {\displaystyle{\displaystyle|v|<|u|}}
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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.m2adec
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    Q11430
    Defining formula
    𝒞 ν ⁡ ( z ) cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.Px5.p1.m3aadec
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    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1adec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1adec
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