DLMF:10.60.E11 (Q3786)

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DLMF:10.60.E11
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    Statements

    test
    ∑ n = 0 ∞ 𝗃 n 2 ⁡ ( z ) = Si ⁡ ( 2 ⁢ z ) 2 ⁢ z . superscript subscript 𝑛 0 spherical-Bessel-J 𝑛 2 𝑧 sine-integral 2 𝑧 2 𝑧 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}{\mathsf{j}_{n}^{2}}\left(z% \right)=\frac{\mathrm{Si}\left(2z\right)}{2z}.}}
    0 references
    DLMF id
    DLMF:10.60.E11
    0 references
    Symbols used
    sine integral
    test
    Si ⁡ ( z ) sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E9.m2adec
    0 references
    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.m2afdec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1jdec
    0 references
     
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