Geodesic
Domains of convergence for $A$-hypergeometric series and integrals
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 509-529.

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We prove two theorems on the domains of convergence for $A$-hypergeometric series and for associated Mellin–Barnes type integrals. The exact convergence domains are described in terms of amoebas and coamoebas of the corresponding principal $A$-determinants.
Keywords: $A$-hypergeometric series, Mellin–Barnes integral, $\Gamma$-integral
Mots-clés : principal $A$-determinant. 
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Lisa Nilsson; Mikael Passare; August K. Tsikh. Domains of convergence for $A$-hypergeometric series and integrals. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 509-529. http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a13/

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