DLMF:10.44.E3 (Q3651)

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DLMF:10.44.E3
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    Statements

    test
    𝒵 ν ⁡ ( u ± v ) = ∑ k = - ∞ ∞ ( ± 1 ) k ⁢ 𝒵 ν + k ⁡ ( u ) ⁢ I k ⁡ ( v ) , modified-cylinder-function 𝜈 plus-or-minus 𝑢 𝑣 superscript subscript 𝑘 superscript plus-or-minus 1 𝑘 modified-cylinder-function 𝜈 𝑘 𝑢 modified-Bessel-first-kind 𝑘 𝑣 {\displaystyle{\displaystyle\mathscr{Z}_{\nu}\left(u\pm v\right)=\sum_{k=-% \infty}^{\infty}(\pm 1)^{k}\mathscr{Z}_{\nu+k}\left(u\right)I_{k}\left(v\right% ),}}
    0 references
    DLMF id
    DLMF:10.44.E3
    0 references
    constraint
    | v | < | u | 𝑣 𝑢 {\displaystyle{\displaystyle|v|<|u|}}
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    Symbols used
    modified Bessel function of the first kind
    test
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2aadec
    0 references
    Q11413
    test
    𝒵 ν ⁡ ( z ) modified-cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{Z}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.Px2.p1.m3aadec
    0 references
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1bdec
    0 references
     
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