DLMF:10.60.E2 (Q3777)

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DLMF:10.60.E2
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    Statements

    test
    sin ⁡ w w = ∑ n = 0 ∞ ( 2 ⁢ n + 1 ) ⁢ 𝗃 n ⁡ ( v ) ⁢ 𝗃 n ⁡ ( u ) ⁢ P n ⁡ ( cos ⁡ α ) . 𝑤 𝑤 superscript subscript 𝑛 0 2 𝑛 1 spherical-Bessel-J 𝑛 𝑣 spherical-Bessel-J 𝑛 𝑢 shorthand-Legendre-P-first-kind 𝑛 𝛼 {\displaystyle{\displaystyle\frac{\sin w}{w}=\sum_{n=0}^{\infty}(2n+1)\mathsf{% j}_{n}\left(v\right)\mathsf{j}_{n}\left(u\right)P_{n}\left(\cos\alpha\right).}}
    0 references
    DLMF id
    DLMF:10.60.E2
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    Symbols used
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    Q11447
    test
    P ν ⁡ ( z ) = P ν 0 ⁡ ( z ) shorthand-Legendre-P-first-kind 𝜈 𝑧 Legendre-P-first-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m3aadec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
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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.m2aadec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1adec
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