Barnes-Ismagilov integrals and hypergeometric functions of the complex field

Abstract

We examine a family ${}_p{G}_q^{\mathbb{C}}[\genfrac{}{}{0ex}{}{(a)}{(b)};z]$ 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 ${}_p{G}_q^{\mathbb{C}}(z)$ as quadratic expressions in the generalized hypergeometric functions ${}_p{F}_{q-1}$ and discuss further properties of the functions ${}_p{G}_q^{\mathbb{C}}(z)$.

References in corpus (6)

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• On Complex Gamma-Function Integrals
• The Endless Beta Integrals
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Cited by in corpus (9)

• On Complex Gamma-Function Integrals
• The Endless Beta Integrals
• Elliptic hypergeometric function and $6j$-symbols for the SL(2,$\mathbb{C}$) group
• Mellin$-$Barnes Transformation for Two-Loop Master-Diagram
• On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions
• Complex and rational hypergeometric functions on root systems
• The Gelfand-Tsetlin basis for infinite-dimensional representations of $g{l}_n(\mathbb{C})$
• BC-type open $SL(2,\mathbb{C})$ spin chain
• From hyperbolic to complex Euler integrals