×

Analytic continuation formulas and Jacobi-type relations for Lauricella function. (English. Russian original) Zbl 1350.33021

Dokl. Math. 93, No. 2, 129-134 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 467, No. 1, 7-12 (2016).
This paper is a continuation of the author’s earlier works. The Lauricella function \(F_D\) for \(N\) variables is considered. Analytic continuations beyond the boundary of the unit polydisk is discussed. Continuation formulae are obtained in the neighborhoods of the singular points \(Z^{(1)}=(1,\dots,1)\) and \(Z^\infty=(\infty,\dots,\infty)\). Mellin-Barnes type representation for the Lauricella function \(F_D\) is used in deriving the results. The cases of simple pole situations are considered.

MSC:

33C65 Appell, Horn and Lauricella functions
32D15 Continuation of analytic objects in several complex variables
32S05 Local complex singularities
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lauricella, G., No article title, Rend. Circ. Math. Palermo, 7, 111-158 (1893) · JFM 25.0756.01 · doi:10.1007/BF03012437
[2] H. Exton, Multiple Hypergeometric Functions and Application (Wiley, New York, 1976). · Zbl 0337.33001
[3] K. Iwasaki, H. Kimura, Sh. Shimomura, and M. Yoshida, From Gauss to Painlevé. A Modern Theory of Special Functions (Vieweg, Braunschweig, 1991). · Zbl 0743.34014 · doi:10.1007/978-3-322-90163-7
[4] Higher Transcendental Functions (Bateman Manuscript Project), Ed. by A. Erdelyi (McGraw-Hill, New York, 1953; Nauka, Moscow, 1973), Vol. 1, Chaps. 2, 3. · Zbl 0052.29502
[5] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge Univ. Press, Cambridge, 1927; Editorial URSS, Moscow, 2002), Vol. 2. · JFM 45.0433.02
[6] Appel, P., No article title, J. Math. Pures Appl., Ser. 3, 8, 173-216 (1882) · JFM 14.0375.01
[7] P. Appel and J. Kampé de Feriet, Fonctions hypergéometriques et hypersphérique (Gauthier, Paris, 1926). · JFM 52.0361.13
[8] Bezrodnykh, S. I.; Vlasov, V. I., No article title, Spectr. Evolut. Probl., 16, 112-118 (2006)
[9] L. N. Trefethen and T. A. Driscoll, Schwarz-Christoffel Mapping (Cambridge Univ. Press, Cambridge, 2005). · Zbl 1003.30005
[10] Olson, O. M., No article title, J. Math. Phys., 5, 420-430 (1964) · Zbl 0122.31501 · doi:10.1063/1.1704134
[11] V. I. Vlasov, Doctoral Dissertation in Mathematics and Physics (Comput. Center, Acad. Sci. SSSR, Moscow, 1990).
[12] S. I. Bezrodnykh, in Abstracts of International Conference on Differential Equations and Dynamical Systems, Suzdal, Russia, 2008 (Suzdal, 2008), pp. 34-36.
[13] S. I. Bezrodnykh, Abstracts of 3rd International Conference “Mathematical Ideas of P.L. Chebyshev and Their Application to Current Problems of Natural Science,” Obninsk, Russia, 2006 (Obninsk, 2006), pp. 18-19.
[14] S. I. Bezrodnykh, Candidate’s Dissertation in Mathematics and Physics (Comput. Center, Russ. Acad. Sci., Moscow, 2006).
[15] Brychkov, Yu. A.; Saad, N., No article title, Integral Transforms Special Funct., 23, 793-802 (2012) · Zbl 1257.33028 · doi:10.1080/10652469.2011.636651
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.