DLMF:10.49.E2 (Q3692)

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DLMF:10.49.E2
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    𝗃 n ⁡ ( z ) = sin ⁡ ( z - 1 2 ⁢ n ⁢ π ) ⁢ ∑ k = 0 ⌊ n / 2 ⌋ ( - 1 ) k ⁢ a 2 ⁢ k ⁢ ( n + 1 2 ) z 2 ⁢ k + 1 + cos ⁡ ( z - 1 2 ⁢ n ⁢ π ) ⁢ ∑ k = 0 ⌊ ( n - 1 ) / 2 ⌋ ( - 1 ) k ⁢ a 2 ⁢ k + 1 ⁢ ( n + 1 2 ) z 2 ⁢ k + 2 . spherical-Bessel-J 𝑛 𝑧 𝑧 1 2 𝑛 𝜋 superscript subscript 𝑘 0 𝑛 2 superscript 1 𝑘 subscript 𝑎 2 𝑘 𝑛 1 2 superscript 𝑧 2 𝑘 1 𝑧 1 2 𝑛 𝜋 superscript subscript 𝑘 0 𝑛 1 2 superscript 1 𝑘 subscript 𝑎 2 𝑘 1 𝑛 1 2 superscript 𝑧 2 𝑘 2 {\displaystyle{\displaystyle\mathsf{j}_{n}\left(z\right)=\sin\left(z-\tfrac{1}% {2}n\pi\right)\sum_{k=0}^{\left\lfloor n/2\right\rfloor}(-1)^{k}\frac{a_{2k}(n% +\tfrac{1}{2})}{z^{2k+1}}+\cos\left(z-\tfrac{1}{2}n\pi\right)\sum_{k=0}^{\left% \lfloor(n-1)/2\right\rfloor}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+2}}.}}
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    DLMF:10.49.E2
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