DLMF:10.60.E13 (Q3788)

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DLMF:10.60.E13
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    Statements

    Defining formula
    ∑ n = 0 ∞ ( - 1 ) n ⁢ ( 2 ⁢ n + 1 ) ⁢ 𝗃 n 2 ⁡ ( z ) = sin ⁡ ( 2 ⁢ z ) 2 ⁢ z , superscript subscript 𝑛 0 superscript 1 𝑛 2 𝑛 1 spherical-Bessel-J 𝑛 2 𝑧 2 𝑧 2 𝑧 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}(-1)^{n}(2n+1){\mathsf{j}_{n}^{% 2}}\left(z\right)=\frac{\sin\left(2z\right)}{2z},}}
    0 references
    DLMF id
    DLMF:10.60.E13
    0 references
    Symbols used
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
    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.m2ahdec
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    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1ldec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1idec
    0 references
     
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