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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     author = {Lisa Nilsson and Mikael Passare and August K. Tsikh},
     title = {Domains of convergence for $A$-hypergeometric series and integrals},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     publisher = {mathdoc},
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     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a13/}
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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/