DLMF:10.49.E6 (Q3700)

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DLMF:10.49.E6
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    Statements

    test
    𝗁 n ( 1 ) ⁡ ( z ) = e i ⁢ z ⁢ ∑ k = 0 n i k - n - 1 ⁢ a k ⁢ ( n + 1 2 ) z k + 1 , spherical-Hankel-H-1-Bessel-third-kind 𝑛 𝑧 superscript 𝑒 𝑖 𝑧 superscript subscript 𝑘 0 𝑛 superscript 𝑖 𝑘 𝑛 1 subscript 𝑎 𝑘 𝑛 1 2 superscript 𝑧 𝑘 1 {\displaystyle{\displaystyle{\mathsf{h}^{(1)}_{n}}\left(z\right)=e^{iz}\sum_{k% =0}^{n}i^{k-n-1}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}},}}
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    DLMF id
    DLMF:10.49.E6
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    Symbols used
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    spherical Bessel function of the third kind
    test
    𝗁 n ( 1 ) ⁡ ( z ) spherical-Hankel-H-1-Bessel-third-kind 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{h}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E5.m2adec
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    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1cdec
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    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1cdec
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    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1ddec
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