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Does the integral $ \frac{1}{2\pi i}\int\limits_{a-i\infty}^{a+i \infty}\varGamma^k(z) u^{-z}dz=... $ exist for all complex value $u$, i.e. Meijer-G function defined for the complex values? What does mean $0^{\otimes k}$? For the second integral $ \frac{1}{2\pi i}\int\limits_{a-i\infty}^{a+i \infty}\varGamma^2(z) u^{-z}dz=2K_0(\sqrt u). $ What kind of Bessel function is $K_0$? Does the second equation valid only for real $u$?
