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We examine a family ${}_pG_{q}^{\mathbbC}\big[\genfrac{}{}{0pt}{}{(a)}{(b)};z\big]$ of integrals of Mellin-Barnes typeover the space ${\mathbb Z}\times {\mathbb R}$, such functions $G$ naturallyarise in representation theory of the Lorentz group. We express${}_pG_{q}^{\mathbb C}(z)$ as quadratic expressions in the generalizedhypergeometric functions ${}_{p}F_{q-1}$ and discuss further properties of thefunctions ${}_pG_{q}^{\mathbb C}(z)$.

Barnes-Ismagilov integrals and hypergeometric functions of the complex field