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Barnes-Ismagilov integrals and hypergeometric functions of the complex field
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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 ${}_pG_{q}^{\mathbb C}(z)$.
Forward citations
Cited by 2 Pith papers
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From hyperbolic to complex Euler integrals
Uniform bounds on hyperbolic-gamma ratios justify the degeneration of the univariate hyperbolic beta integral and conical function to complex Euler integrals over the plane.
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On Complex Gamma-Function Integrals
Two complex gamma-function integral identities are proved directly and shown to imply star-triangle relations and the Dotsenko-Fateev duality in a classical limit.
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