DLMF:10.32.E14 (Q3534)

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DLMF:10.32.E14
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    K ν ( z ) = 1 2 π 2 i ( π 2 z ) 1 2 e - z cos ( ν π ) - i i Γ ( t ) Γ ( 1 2 - t - ν ) Γ ( 1 2 - t + ν ) ( 2 z ) t d t , modified-Bessel-second-kind 𝜈 𝑧 1 2 superscript 𝜋 2 𝑖 superscript 𝜋 2 𝑧 1 2 superscript 𝑒 𝑧 𝜈 𝜋 superscript subscript 𝑖 𝑖 Euler-Gamma 𝑡 Euler-Gamma 1 2 𝑡 𝜈 Euler-Gamma 1 2 𝑡 𝜈 superscript 2 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle K_{\nu}\left(z\right)=\frac{1}{2\pi^{2}i}\left(% \frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\cos\left(\nu\pi\right)\*\int_{-i% \infty}^{i\infty}\Gamma\left(t\right)\Gamma\left(\tfrac{1}{2}-t-\nu\right)% \Gamma\left(\tfrac{1}{2}-t+\nu\right)(2z)^{t}\mathrm{d}t,}}
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    DLMF:10.32.E14
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