DLMF:12.5.E1 (Q4115)

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DLMF:12.5.E1
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    Defining formula
    U ⁡ ( a , z ) = e - 1 4 ⁢ z 2 Γ ⁡ ( 1 2 + a ) ⁢ ∫ 0 ∞ t a - 1 2 ⁢ e - 1 2 ⁢ t 2 - z ⁢ t ⁢ d t , parabolic-U 𝑎 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 Euler-Gamma 1 2 𝑎 superscript subscript 0 superscript 𝑡 𝑎 1 2 superscript 𝑒 1 2 superscript 𝑡 2 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle U\left(a,z\right)=\frac{e^{-\frac{1}{4}z^{2}}}{% \Gamma\left(\frac{1}{2}+a\right)}\int_{0}^{\infty}t^{a-\frac{1}{2}}e^{-\frac{1% }{2}t^{2}-zt}\mathrm{d}t,}}
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    DLMF id
    DLMF:12.5.E1
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