DLMF:12.7.E2 (Q4125)

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DLMF:12.7.E2
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    U ⁡ ( - n - 1 2 , z ) = D n ⁡ ( z ) = e - 1 4 ⁢ z 2 ⁢ 𝐻𝑒 n ⁡ ( z ) = 2 - n / 2 ⁢ e - 1 4 ⁢ z 2 ⁢ H n ⁡ ( z / 2 ) , parabolic-U 𝑛 1 2 𝑧 Whittaker-D 𝑛 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 Hermite-polynomial-He 𝑛 𝑧 superscript 2 𝑛 2 superscript 𝑒 1 4 superscript 𝑧 2 Hermite-polynomial-H 𝑛 𝑧 2 {\displaystyle{\displaystyle U\left(-n-\tfrac{1}{2},z\right)=D_{n}\left(z% \right)=e^{-\frac{1}{4}z^{2}}\mathit{He}_{n}\left(z\right)=2^{-n/2}e^{-\frac{1% }{4}z^{2}}H_{n}\left(z/\sqrt{2}\right),}}
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    DLMF:12.7.E2
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