DLMF:13.8.E8 (Q4433)

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DLMF:13.8.E8
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    U ( a , b , x ) = 2 e 1 2 x Γ ( a ) ( 2 β tanh ( w 2 ) ( 1 - e - w β ) - b β 1 - b K 1 - b ( 2 β a ) + a - 1 ( a - 1 + β 1 + β ) 1 - b e - 2 β a O ( 1 ) ) , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑥 2 superscript 𝑒 1 2 𝑥 Euler-Gamma 𝑎 2 𝛽 𝑤 2 superscript 1 superscript 𝑒 𝑤 𝛽 𝑏 superscript 𝛽 1 𝑏 modified-Bessel-second-kind 1 𝑏 2 𝛽 𝑎 superscript 𝑎 1 superscript superscript 𝑎 1 𝛽 1 𝛽 1 𝑏 superscript 𝑒 2 𝛽 𝑎 Big-O 1 {\displaystyle{\displaystyle U\left(a,b,x\right)=\frac{2e^{\frac{1}{2}x}}{% \Gamma\left(a\right)}\left(\sqrt{\frac{2}{\beta}\tanh\left(\frac{w}{2}\right)}% \left(\frac{1-e^{-w}}{\beta}\right)^{-b}\beta^{1-b}K_{1-b}\left(2\beta a\right% )+a^{-1}\left(\frac{a^{-1}+\beta}{1+\beta}\right)^{1-b}e^{-2\beta a}O\left(1% \right)\right),}}
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    DLMF:13.8.E8
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