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A Class of Generalized Hypergeometric Functions in Several Variables

Published online by Cambridge University Press:  20 November 2018

Zhimin Yan
Zhimin Yan*
Affiliation:
Department of Mathematics, Graduate School of City University of New York, 33 W. 42 Street, New York, New York 10036, U.S.A.
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Abstract

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We study a class of generalized hypergeometric functions in several variables introduced by A. Korânyi. It is shown that the generalized Gaussian hypergeometric function is the unique solution of a system partial differential equations. Analogues of some classical results such as Kummer relations and Euler integral representations are established. Asymptotic behavior of generalized hypergeometric functions is obtained which includes some known estimates.

Keywords

33A3033A4032A99
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 6 , 01 December 1992 , pp. 1317 - 1338
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Constantine, A.G., Some noncentral distribution problems in multivariate analysis, Ann. Math. Statist. 34(1963),1270–1285.Google Scholar
2. Faraut, J. and Korányi, A., Function spaces and reproducing kernels on bounded symmetric domains, J. Functional Analysis 88(1990), 64–89.Google Scholar
3. Faraut, J., Fonctions hypergéométrique s associées aux cônes symétriques, C.R. Acad. Sci. Paris 307(1988), 555–558.Google Scholar
4. Gross, K. and Richards, D., Special functions of matrix argument I, Tran. Amer. Math. Soc. 301(1987), 781–811.Google Scholar
5. Herz, C.S., Bessel functions of matrix argument, Ann. of Math. (3) 61(1955), 474–523.Google Scholar
6. Kadell, K.W., Selberg-Jackpolynomials, preprint.Google Scholar
7. Kor, A.ányi, Hua-type integrals, hypergeometric functions and symmetric polynomials, preprint.Google Scholar
8. Macdonald, I.G., Commuting differential operators and zonal spherical functions, Algebraic Group, Utrecht 1986, Springer Lecture Notes in Mathematics 1271(1987), 189–200.Google Scholar
9. Mitchell, J., Singular Integrals on Bounded Symmetric Domains II, Contemporay Mathematics 9(1982), 327–331.Google Scholar
10. Mitchell, J. and Sampson, G., Singular Integrals on Bounded Symmetric Domains in C”, J. Mathematical Analysis and Applications 90( 1982), 371–380.Google Scholar
11. Muirhead, R.J., Aspects of multivariate statistical theory, J. Wiley, New York, 1982.Google Scholar
12. R, R. Stanley, Some combinatorial propertities of Jack symmetric functions, Adv. in Math. 77(1989), 76–115.Google Scholar
13. Yan, Z., Generalized hypergeometric functions, C.R. Acad. Sci. Paris (I) 310(1990), 349–354.Google Scholar
14. Yan, Z., Generalized Hypergeometric Functions and La guerre Polynomials in Two Variables, Contemporary Mathematics, to appear.Google Scholar