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J. Sib. Fed. Univ. Math. Phys., 2019, Volume 12, Issue 4, Pages 509–529 (Mi jsfu784)  

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

Lisa Nilssona, Mikael Passarea, August K. Tsikhb

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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.2604.2017/PCh
Russian Foundation for Basic Research 18-51-41011_Uzb_t
The third author was supported by the grant of Ministry of Education and Science of the Russian Federation (no. 1.2604.2017/PCh) and was supported by RFBR, grant 18-51-41011 Uzb.t.


DOI: https://doi.org/10.17516/1997-1397-2019-12-4-509-529

Full text: PDF file (196 kB)
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Bibliographic databases:

UDC: 517.55+512.761
Received: 17.05.2019
Received in revised form: 10.07.2019
Accepted: 15.08.2019
Language:

Citation: Lisa Nilsson, Mikael Passare, August K. Tsikh, “Domains of convergence for $A$-hypergeometric series and integrals”, J. Sib. Fed. Univ. Math. Phys., 12:4 (2019), 509–529

Citation in format AMSBIB
\Bibitem{NilPasTsi19}
\by Lisa~Nilsson, Mikael~Passare, August~K.~Tsikh
\paper Domains of convergence for $A$-hypergeometric series and integrals
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2019
\vol 12
\issue 4
\pages 509--529
\mathnet{http://mi.mathnet.ru/jsfu784}
\crossref{https://doi.org/10.17516/1997-1397-2019-12-4-509-529}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000483323900014}


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  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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