DLMF:6.10.E4 (Q2281)

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DLMF:6.10.E4
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    Statements

    Defining formula
    Si ⁡ ( z ) = z ⁢ ∑ n = 0 ∞ ( 𝗃 n ⁡ ( 1 2 ⁢ z ) ) 2 , sine-integral 𝑧 𝑧 superscript subscript 𝑛 0 superscript spherical-Bessel-J 𝑛 1 2 𝑧 2 {\displaystyle{\displaystyle\mathrm{Si}\left(z\right)=z\sum_{n=0}^{\infty}% \left(\mathsf{j}_{n}\left(\tfrac{1}{2}z\right)\right)^{2},}}
    0 references
    DLMF id
    DLMF:6.10.E4
    0 references
    Symbols used
    sine integral
    Defining formula
    Si ⁡ ( z ) sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E9.m2adec
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    spherical Bessel function of the first kind
    Defining formula
    𝗃 n ⁡ ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E3.m2adec
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    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1adec
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    Q11308
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C6.S1.XMD3.m1dec
    0 references
     
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