DLMF:10.23.E12 (Q3466)

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DLMF:10.23.E12
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    Statements

    test
    1 t - z = J 0 ⁡ ( z ) ⁢ O 0 ⁡ ( t ) + 2 ⁢ ∑ k = 1 ∞ J k ⁡ ( z ) ⁢ O k ⁡ ( t ) , 1 𝑡 𝑧 Bessel-J 0 𝑧 Neumann-polynomial 0 𝑡 2 superscript subscript 𝑘 1 Bessel-J 𝑘 𝑧 Neumann-polynomial 𝑘 𝑡 {\displaystyle{\displaystyle\frac{1}{t-z}=J_{0}\left(z\right)O_{0}\left(t% \right)+2\sum_{k=1}^{\infty}J_{k}\left(z\right)O_{k}\left(t\right),}}
    0 references
    DLMF id
    DLMF:10.23.E12
    0 references
    constraint
    | z | < | t | 𝑧 𝑡 {\displaystyle{\displaystyle|z|<|t|}}
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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.m2ahdec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1bdec
    0 references
     
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