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arXiv · 1910.10686

Barnes-Ismagilov integrals and hypergeometric functions of the complex field

Yury A. Neretin
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Abstract

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

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Yury A. Neretin. 2019-10-23. Barnes-Ismagilov integrals and hypergeometric functions of the complex field. https://doi.org/10.3842/sigma.2020.072

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