DLMF:10.60.E1 (Q3776)

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DLMF:10.60.E1
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    Statements

    Defining formula
    cos ⁡ w w = - ∑ n = 0 ∞ ( 2 ⁢ n + 1 ) ⁢ 𝗃 n ⁡ ( v ) ⁢ 𝗒 n ⁡ ( u ) ⁢ P n ⁡ ( cos ⁡ α ) , 𝑤 𝑤 superscript subscript 𝑛 0 2 𝑛 1 spherical-Bessel-J 𝑛 𝑣 spherical-Bessel-Y 𝑛 𝑢 shorthand-Legendre-P-first-kind 𝑛 𝛼 {\displaystyle{\displaystyle\frac{\cos w}{w}=-\sum_{n=0}^{\infty}(2n+1)\mathsf% {j}_{n}\left(v\right)\mathsf{y}_{n}\left(u\right)P_{n}\left(\cos\alpha\right),}}
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    DLMF id
    DLMF:10.60.E1
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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
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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