DLMF:10.60.E3 (Q3778)

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DLMF:10.60.E3
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    Statements

    test
    e - w w = 2 π ⁢ ∑ n = 0 ∞ ( 2 ⁢ n + 1 ) ⁢ 𝗂 n ( 1 ) ⁡ ( v ) ⁢ 𝗄 n ⁡ ( u ) ⁢ P n ⁡ ( cos ⁡ α ) , superscript 𝑒 𝑤 𝑤 2 𝜋 superscript subscript 𝑛 0 2 𝑛 1 spherical-Bessel-I-1 𝑛 𝑣 spherical-Bessel-K 𝑛 𝑢 shorthand-Legendre-P-first-kind 𝑛 𝛼 {\displaystyle{\displaystyle\frac{e^{-w}}{w}=\frac{2}{\pi}\sum_{n=0}^{\infty}(% 2n+1){\mathsf{i}^{(1)}_{n}}\left(v\right)\mathsf{k}_{n}\left(u\right)P_{n}% \left(\cos\alpha\right),}}
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    DLMF id
    DLMF:10.60.E3
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    constraint
    | v ⁢ e ± i ⁢ α | < | u | 𝑣 superscript 𝑒 plus-or-minus 𝑖 𝛼 𝑢 {\displaystyle{\displaystyle|ve^{\pm i\alpha}|<|u|}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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