DLMF:10.49.E10 (Q3706)

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DLMF:10.49.E10
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    Statements

    test
    𝗂 n ( 2 ) ⁡ ( z ) = 1 2 ⁢ e z ⁢ ∑ k = 0 n ( - 1 ) k ⁢ a k ⁢ ( n + 1 2 ) z k + 1 + ( - 1 ) n ⁢ 1 2 ⁢ e - z ⁢ ∑ k = 0 n a k ⁢ ( n + 1 2 ) z k + 1 . spherical-Bessel-I-2 𝑛 𝑧 1 2 superscript 𝑒 𝑧 superscript subscript 𝑘 0 𝑛 superscript 1 𝑘 subscript 𝑎 𝑘 𝑛 1 2 superscript 𝑧 𝑘 1 superscript 1 𝑛 1 2 superscript 𝑒 𝑧 superscript subscript 𝑘 0 𝑛 subscript 𝑎 𝑘 𝑛 1 2 superscript 𝑧 𝑘 1 {\displaystyle{\displaystyle{\mathsf{i}^{(2)}_{n}}\left(z\right)=\tfrac{1}{2}e% ^{z}\sum_{k=0}^{n}(-1)^{k}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}+(-1)^{n}\tfrac{% 1}{2}e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}.}}
    0 references
    DLMF id
    DLMF:10.49.E10
    0 references
    Symbols used
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    modified spherical Bessel function
    test
    𝗂 n ( 2 ) ⁡ ( z ) spherical-Bessel-I-2 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E8.m2adec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1fdec
    0 references
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1fdec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1hdec
    0 references
    expansion (locally)
    test
    a k ⁢ ( ν ) subscript 𝑎 𝑘 𝜈 {\displaystyle{\displaystyle a_{k}(\nu)}}
    xml-id
    C10.S17.XMD1.m1fdec
    0 references
     
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