DLMF:13.10.E16 (Q4475)

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DLMF:13.10.E16
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    test
    ∫ 0 ∞ e - t ⁢ t 1 2 ⁢ ν ⁢ U ⁡ ( a , b , t ) ⁢ J ν ⁡ ( 2 ⁢ x ⁢ t ) ⁢ d t = Γ ⁡ ( ν - b + 2 ) ⁢ x 1 2 ⁢ ν ⁢ e - x ⁢ 𝐌 ⁡ ( a , a - b + ν + 2 , x ) , superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑡 1 2 𝜈 Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑡 Bessel-J 𝜈 2 𝑥 𝑡 𝑡 Euler-Gamma 𝜈 𝑏 2 superscript 𝑥 1 2 𝜈 superscript 𝑒 𝑥 Kummer-confluent-hypergeometric-bold-M 𝑎 𝑎 𝑏 𝜈 2 𝑥 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-t}t^{\frac{1}{2}\nu}U\left(a,% b,t\right)J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d}t=\Gamma\left(\nu-b+2\right)% x^{\frac{1}{2}\nu}e^{-x}{\mathbf{M}}\left(a,a-b+\nu+2,x\right),}}
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    DLMF:13.10.E16
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