DLMF:8.21.E16 (Q2738)

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DLMF:8.21.E16
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    Si ( a , z ) = z a k = 0 ( 2 k + 3 2 ) ( 1 - 1 2 a ) k ( 1 2 + 1 2 a ) k + 1 𝗃 2 k + 1 ( z ) , generalized-sine-integral-Si 𝑎 𝑧 superscript 𝑧 𝑎 superscript subscript 𝑘 0 2 𝑘 3 2 Pochhammer 1 1 2 𝑎 𝑘 Pochhammer 1 2 1 2 𝑎 𝑘 1 spherical-Bessel-J 2 𝑘 1 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(a,z\right)=z^{a}\sum_{k=0}^{% \infty}\frac{\left(2k+\frac{3}{2}\right){\left(1-\frac{1}{2}a\right)_{k}}}{{% \left(\frac{1}{2}+\frac{1}{2}a\right)_{k+1}}}\mathsf{j}_{2k+1}\left(z\right),}}
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    a - 1 , - 3 , - 5 , 𝑎 1 3 5 {\displaystyle{\displaystyle a\neq-1,-3,-5,\dots}}
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