DLMF:12.9.E2 (Q4151)

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DLMF:12.9.E2
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    V ⁡ ( a , z ) ∼ 2 π ⁢ e 1 4 ⁢ z 2 ⁢ z a - 1 2 ⁢ ∑ s = 0 ∞ ( 1 2 - a ) 2 ⁢ s s ! ⁢ ( 2 ⁢ z 2 ) s , asymptotic-expansion parabolic-V 𝑎 𝑧 2 𝜋 superscript 𝑒 1 4 superscript 𝑧 2 superscript 𝑧 𝑎 1 2 superscript subscript 𝑠 0 Pochhammer 1 2 𝑎 2 𝑠 𝑠 superscript 2 superscript 𝑧 2 𝑠 {\displaystyle{\displaystyle V\left(a,z\right)\sim\sqrt{\frac{2}{\pi}}e^{\frac% {1}{4}z^{2}}z^{a-\frac{1}{2}}\sum_{s=0}^{\infty}\frac{{\left(\frac{1}{2}-a% \right)_{2s}}}{s!(2z^{2})^{s}},}}
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    DLMF:12.9.E2
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