DLMF:10.56.E5 (Q3769)

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DLMF:10.56.E5
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    test
    exp ⁡ ( - z 2 + 2 ⁢ i ⁢ z ⁢ t ) z = e - z z + 2 π ⁢ ∑ n = 1 ∞ ( - i ⁢ t ) n n ! ⁢ 𝗄 n - 1 ⁡ ( z ) . superscript 𝑧 2 2 𝑖 𝑧 𝑡 𝑧 superscript 𝑒 𝑧 𝑧 2 𝜋 superscript subscript 𝑛 1 superscript 𝑖 𝑡 𝑛 𝑛 spherical-Bessel-K 𝑛 1 𝑧 {\displaystyle{\displaystyle\frac{\exp\left(-\sqrt{z^{2}+2izt}\right)}{z}=% \frac{e^{-z}}{z}+\frac{2}{\pi}\sum_{n=1}^{\infty}\frac{(-it)^{n}}{n!}\mathsf{k% }_{n-1}\left(z\right).}}
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    DLMF:10.56.E5
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