58
Views
5
CrossRef citations to date
0
Altmetric
Research Articles

Analytic continuation of Lauricella's function FD(N) for large in modulo variables near hyperplanes {zj = zl}

Pages 276-291 | Received 28 Apr 2021, Accepted 10 May 2021, Published online: 19 May 2021

References

  • Lauricella G. Sulle funzioni ipergeometriche a piu variabili. Rend Circ Mat Palermo. 1893;7:111–158.
  • Appell P, Kampé de Fériet J. Fonctions hypergéometriques et hypersphérique. Paris: Gauthier–Villars; 1926.
  • Bateman H, Erdélyi A. Higher transcendental functions. Vol. 1. The hypergeometric function, Legendre functions. New York–Toronto–London: McGraw–Hill; 1953.
  • Exton H. Multiple hypergeometric functions and application. New York: John Willey & Sons, Inc; 1976.
  • Srivastava HM, Karlsson PW. Multiple Gaussian hypergeometric series. Chichester: Ellis Horwood; 1985.
  • Gel'fand IM, Graev MI, Retakh VS. General hypergeometric systems of equations and series of hypergeometric type. Russ Math Surv. 1992;47(4):1–88.
  • Iwasaki K, Kimura H, Shimomura Sh, et al. From Gauss to Painlevé: a modern theory of special functions. Braunschweig: Friedrich Vieweg & Sohn; 1991. (Aspects of mathematics; vol. E16).
  • Aomoto K, Kita M. Theory of hypergeometric functions. Tokyo, Dordrecht, Heidelberg: Springer; 2011. (Springer monographs in mathematics).
  • Olsson OM. Integration of the partial differential equations for the hypergeometric function F1 and FD of two and more variables. J Math Phys. 1964;5(3):420–430.
  • Bezrodnykh SI. The Lauricella hypergeometric function FD(N), the Riemann–Hilbert problem, and some applications. Russ Math Surv. 2018;73(6):941–1031.
  • Bezrodnykh SI. Analytic continuation of the Lauricella function FD(N) with arbitrary number of variables. Integr Transf Spec F. 2018;29(1):21–42.
  • Bezrodnykh SI. Analytic continuation of the Appell function F1 and integration of the associated system of equations in the logarithmic case. Comput Math Math Phys. 2017;57(4):559–589.
  • Sadykov TM, Tsikh AK. Hypergeometric and algebraic functions in several variables. Moscow: Nauka; 2014. (In Russian).
  • Kuznetsov VB, Sklyanon EK. Eigenproblem for Jacobi matrices: hypergeometric series solution. Philos Trans R Soc A. 2008;366:1089–1114.
  • Tarasov OV. Using functional equations to calculate Feynman integrals. Theoret Math Phys. 2019;200(2):1205–1221.
  • Bytev VV, Kniehl BA. Derivatives of any Horn-type hypergeometric functions with respect to their parameters. Nucl Phys B. 2020. DOI:https://doi.org/10.1016/j.nuclphysb.2019.114911
  • Brychkov YuA, Savischenko NV. On some formulas for the Horn functions G1(a,b,b′;w,z) and Γ2(b,b′;w,z). Integral Transf Spec F. 2020. DOI:https://doi.org/10.1080/10652469.2020.1746051
  • Brychkov YuA, Savischenko NV. On some formulas for the Horn functions H1(a,b,c;d;w,z) and H1(c)(a,b;d;w,z). Integr Transf Spec F. 2020. DOI:https://doi.org/10.1080/10652469.2020.1790554
  • Brychkov YuA, Savischenko NV. On some formulas for the Horn functions H3(a,b;c;w,z), H6(c)(a;c;w,z) and Humbert function Φ3(b;c;w,z). Integr Transf Spec F. 2020. DOI:https://doi.org/10.1080/10652469.2020.1835893
  • Kalmykov M, Bytev V, Kniehl B, et al. Hypergeometric functions and Feynman diagrams. 2020. arXiv:2012.14492.
  • Bezrodnykh SI. Analytic continuation of the Horn hypergeometric series with an arbitrary number of variables. Integr Transf Spec F. 2020. DOI:https://doi.org/10.1080/10652469.2020.1744590
  • Vlasov VI. Boundary value problems in domains with curvilinear boundary [doctoral thesis]. Moscow: Computing Center, Academy of Sciences of the USSR; 1990. (In Russian).
  • Brychkov YuA, Savischenko NV. Application of hypergeometric functions of two variables in wireless communication theory. Lobachevskii J Math. 2019;40(7):938–953.
  • Bezrodnykh S, Bogatyrev A, Goreinov S, et al. On capacity computation for symmetric polygonal condensers. J Comput Appl Math. 2019;361:271–282.
  • Berge J, Massey R, Baghi Q, et al. Exponential shapelets: basis functions for data analysis of isolated feature. Mon Not R Astron Soc. 2019;486(1):544–559.
  • Bezrodnykh SI, Vlasov VI. Asymptotics of the Riemann–Hilbert problem for a magnetic reconnection model in plasma. Comput Math Math Phys. 2020;60(11):1839–1854.
  • Vlasov VI, Skorokhodov SL. Analytical solution for the cavitating flow over a wedge. I. Comput Math Math Phys. 2020;60(12):2032–2055.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.