DLMF:10.53.E1 (Q3755)

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DLMF:10.53.E1
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    Statements

    test
    𝗃 n ⁡ ( z ) = z n ⁢ ∑ k = 0 ∞ ( - 1 2 ⁢ z 2 ) k k ! ⁢ ( 2 ⁢ n + 2 ⁢ k + 1 ) !! , spherical-Bessel-J 𝑛 𝑧 superscript 𝑧 𝑛 superscript subscript 𝑘 0 superscript 1 2 superscript 𝑧 2 𝑘 𝑘 double-factorial 2 𝑛 2 𝑘 1 {\displaystyle{\displaystyle\mathsf{j}_{n}\left(z\right)=z^{n}\sum_{k=0}^{% \infty}\frac{(-\frac{1}{2}z^{2})^{k}}{k!(2n+2k+1)!!},}}
    0 references
    DLMF id
    DLMF:10.53.E1
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    constraint
    | z | < ∞ 𝑧 {\displaystyle{\displaystyle|z|<\infty}}
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    Symbols used
    Q11277
    test
    !! double-factorial {\displaystyle{\displaystyle!!}}
    xml-id
    introduction.Sx4.p1.t1.r16.m7adec
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    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    spherical Bessel function of the first kind
    test
    𝗃 n ⁡ ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E3.m2adec
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    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1dec
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