Abstract:
We prove two theorems on the domains of convergence for AA-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 AA-determinants.
Keywords:AA-hypergeometric series, Mellin–Barnes integral, ΓΓ-integral, principal AA-determinant.
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.
Received: 17.05.2019 Received in revised form: 10.07.2019 Accepted: 15.08.2019
Bibliographic databases:
Document Type:
Article
UDC:517.55+512.761
Language: English
Citation:
Lisa Nilsson, Mikael Passare, August K. Tsikh, “Domains of convergence for AA-hypergeometric series and integrals”, J. Sib. Fed. Univ. Math. Phys., 12:4 (2019), 509–529
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\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
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\crossref{https://doi.org/10.17516/1997-1397-2019-12-4-509-529}
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This publication is cited in the following 8 articles:
Irina A. Antipova, Timofey A. Efimov, Avgust K. Tsikh, “Mellin transforms for rational functions with quasi-elliptic denominators”, Zhurn. SFU. Ser. Matem. i fiz., 16:6 (2023), 738–750
Wayne M. Lawton, “An explanation of Mellin's 1921 paper”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 46 (2023), 98–109
Vitaly A. Krasikov, “A Survey on Computational Aspects of Polynomial Amoebas”, Math.Comput.Sci., 17:3-4 (2023)
Špela Špenko, Michel Van den Bergh, “Perverse schobers and GKZ systems”, Advances in Mathematics, 402 (2022), 108307
Artem V. Senashov, “A list of integral representations for diagonals of power series of rational functions”, Zhurn. SFU. Ser. Matem. i fiz., 14:5 (2021), 624–631
B. Ananthanarayan, S. Banik, S. Friot, Sh. Ghosh, “Multiple series representations of N-fold Mellin-Barnes integrals”, Phys. Rev. Lett., 127:15 (2021), 151601
Mikhail Kalmykov, Vladimir Bytev, Bernd A. Kniehl, Sven-Olaf Moch, Bennie F. L. Ward, Scott A. Yost, Texts & Monographs in Symbolic Computation, Anti-Differentiation and the Calculation of Feynman Amplitudes, 2021, 189
A. N. Cherepanskiy, A. K. Tsikh, “Convergence of two-dimensional hypergeometric series for algebraic functions”, Integral Transform. Spec. Funct., 31:10 (2020), 838–855
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