DLMF:12.2.E17 (Q4102)

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DLMF:12.2.E17
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    test
    2 ⁢ π ⁢ U ⁡ ( - a , ± i ⁢ z ) = Γ ⁡ ( 1 2 + a ) ⁢ ( e ∓ i ⁢ π ⁢ ( 1 2 ⁢ a - 1 4 ) ⁢ U ⁡ ( a , z ) + e ± i ⁢ π ⁢ ( 1 2 ⁢ a - 1 4 ) ⁢ U ⁡ ( a , - z ) ) . 2 𝜋 parabolic-U 𝑎 plus-or-minus 𝑖 𝑧 Euler-Gamma 1 2 𝑎 superscript 𝑒 minus-or-plus 𝑖 𝜋 1 2 𝑎 1 4 parabolic-U 𝑎 𝑧 superscript 𝑒 plus-or-minus 𝑖 𝜋 1 2 𝑎 1 4 parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle\sqrt{2\pi}U\left(-a,\pm iz\right)=\Gamma\left(% \tfrac{1}{2}+a\right)\left(e^{\mp i\pi(\frac{1}{2}a-\frac{1}{4})}U\left(a,z% \right)+e^{\pm i\pi(\frac{1}{2}a-\frac{1}{4})}U\left(a,-z\right)\right).}}
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    DLMF id
    DLMF:12.2.E17
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