Lisa Nilsson, Mikael Passare, August K. Tsikh, “Domains of convergence for <nobr>$A$</nobr>-hypergeometric series and integrals”, J. Sib. Fed. Univ. Math. Phys., 2019, Volume 12, Issue 4,Pages <nobr>509

This article is cited in 8 papers

Domains of convergence for $A$-hypergeometric series and integrals

Lisa Nilsson^a, Mikael Passare^a, August K. Tsikh^b

^a Stockholm University, Stockholm, Sweden
^b Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: 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, principal $A$-determinant.

UDC: 517.55+512.761

Received: 17.05.2019
Received in revised form: 10.07.2019
Accepted: 15.08.2019

Language: English

DOI: 10.17516/1997-1397-2019-12-4-509-529