پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 679 |
| تعداد مقالات | 9,900 |
| تعداد مشاهده مقاله | 70,094,907 |
| تعداد دریافت فایل اصل مقاله | 49,419,278 |
Some Gauss type contiguous relations between Faraut-Koranyi hypergeometric functions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 30، دوره 15، شماره 8، آبان 2024، صفحه 349-358 اصل مقاله (422.39 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.24339.2720 | ||
| نویسندگان | ||
| Fouzia EL Wassouli* ؛ Daoud Oukacha | ||
| Department of Mathematics, Faculty of Sciences, University Hassan II, Casablanca, Morocco | ||
| تاریخ دریافت: 03 شهریور 1400، تاریخ پذیرش: 30 مهر 1400 | ||
| چکیده | ||
| In this paper, we give a complete description of the generalized hypergeometric functions, introduced by Faraut and Kor'{a}nyi on the Cartan domain. We establish some Gauss type contiguous relations between these functions on the two Cartan domains of type $I_{ 2}$ and type $IV_{4}$ analogous to the classical relations in the one variable case. | ||
| کلیدواژهها | ||
| Gindikin Gamma function؛ generalized hypergeometric functions؛ zonal polynomials | ||
| مراجع | ||
|
[1] Y. Chikuse, Invariant polynomials with matrix arguments and their applications, Multivar. Statist. Anal. 1 (1980), 54–68. [2] Y. Chikuse and A.W. Davis, Some properties of invariant polynomials with matrix arguments and their applications in econometrics, J. Ann. Inst. Statist. Math. Part A 38 (1986), 109–122. [3] A.G. Constantine, Noncentral distribution problem in multivariante analysis, J. Ann. Math. Statist. 34 (1963), 1270–1285. [4] A.W. Davis, Invariant polynomials with two matrix arguments, extending the zonal polynomials: Applications to multivariante distribution theory, J. Ann. Instit. Statist. Math. Part A 31 (1979), 465–485. [5] A.W. Davis, Invariant polynomials with two matrix arguments, extending the zonal polynomials, Krishnaiah P R (ed.) Multivariante Analysis V. (North-Holland Publishing Company), 1980, pp. 287-299. [6] A. Debiard, Polynomes de Tch´ebichev et de Jacobi dans un espace euclidien de dimension p, C.R. Acad. Sci. Paris 296 (1983), 529–532. [7] F. El Wassouli and Z. Mouhcine, Zonal spherical function on the Lie ball in Cn, J. Integral Transforms Spec. Funct. 30 (2019), 594–600. [8] J. Faraut and A. Koranyi, Fonctions gyperg´eom´etriques associ´es aux cˆones sym´etrique, C. R. Acd. Sci. Paris 307 (1988), 555–558. [9] J.Faraut and A. Koranyi, Functions spaces and reproducing kernels on bounded symmetric domains, J. Funct. Anal, 88 (1990), 64–89. [10] J. Faraut and A. Koranyi, Analysis on Symmetric Cones, Clarendon Press. Oxford, 1994. [11] S. Gindikin, Analysis on homogeneous domains, Russ. Math. Surv, 19 (1964), 1–89. [12] C.S. Herz, Bessel functions of matrix argument, J. Ann. Math. 61 (1955), 474-523. [13] A. Koranyi, Hua-type integrals, hypergeometric functions and symmetric polynomials, Int. Symp. Memory of Hua Loo Keng, Vol.II (Beijing, (1988)). Springer. Berlin, 1991, pp. 169-180. [14] M. Lassalle and M. Schlosser, An analytic formula for Macdonald polynomials, C. R. Math. Acad. Sci. Paris 337 (2003), 569—574. [15] O. Loos, Bounded Symmetric Domains and Jordan Pairs, Univ. of California, Irvine, 1977. [16] L.G. Macdonald, Commuting differential operators and zonal spherical functions, Algebraic Groups Utrecht 1986: Proc. Symp. Honour of TA, Springer Berlin Heidelberg, 2006, pp. 189–200. [17] R.J. Muirhead, Aspects of Multivariate Statistical Theory, John Wiley, 1982. [18] Z. Yan, A class of generalized hypergeometric functions in several variables, Canad. J. Math. 44 (1992), 1317–1338. | ||
|
آمار تعداد مشاهده مقاله: 3,041 تعداد دریافت فایل اصل مقاله: 4,796 |
||