In this paper, we introduce Lauricella matrix functions of three variables as well as n-variables. We also define the matrix analog of the three variables and Srivastava’s triple hypergeometric functions. We examine the regions of convergence of Lauricella matrix functions and Srivastava’s triple hypergeometric matrix functions and also obtain their integral representations.
REFERENCES
1.
Constantine
, A. G.
and Muirhead
, R. J.
, “Partial differential equations for hypergeometric functions of two argument matrices
,” J. Multivar. Anal.
2
, 332
–338
(1972
).2.
Cortés
, J. C.
, Jódar
, L.
, Solís
, F. J.
, and Ku-Carrillo
, R.
, “Infinite matrix products and the representation of the matrix Gamma function
,” Abstr. Appl. Anal.
2015
, 564287
.3.
Dunford
, N.
and Schwartz
, J.
, Linear Operators, Part-I
(Addison-Wesley
, New York
, 1957
).4.
Dwivedi
, R.
and Sahai
, V.
, “On the hypergeometric matrix functions of two variables
,” Linear Multilinear Algebra
1
(2017
).5.
Golub
, G. H.
and Van Loan
, C. F.
, Matrix Computations
(Johns Hopkins University Press
, Baltimore, MD
, 1989
).6.
Higueras
, I.
and Garcia-Celayeta
, B.
, “Logarithmic norms for matrix pencils
,” SIAM J. Matrix Anal. Appl.
20
(3
), 646
–666
(1999
).7.
Hu
, G. D.
and Liu
, M.
, “The weighted logarithmic matrix norm and bounds of the matrix exponential
,” Linear Algebra Appl.
390
, 145
–154
(2004
).8.
James
, A. T.
, “Special functions of matrix and single argument in statistics
,” in Theory and Application of Special Functions
, edited by Askey
, R.
(Academic Press
, New York
, 1975
), pp. 497
–520
, Proceedings of an Advanced Seminar, Mathematical Research Center, University of Wisconsin, Madison, Wisconsin, Publication No. 35.9.
Jódar
, L.
and Cortés
, J. C.
, “On the hypergeometric matrix function
,” in Proceedings of the VIIIth Symposium on Orthogonal Polynomials and Their Applications (Seville, 1997)
[J. Comput. Appl. Math.
99
(1-2
), 205
–217
(1998
)].10.
Jódar
, L.
and Cortés
, J. C.
, “Some properties of Gamma and beta matrix functions
,” Appl. Math. Lett.
11
(1
), 89
–93
(1998
).11.
Lauricella
, G.
, “Sulle funzioni ipergeometriche a piú variabili
,” Rend. Circolo Mat. Palermo
7
, 111
–158
(1893
).12.
13.
Sastre
, J.
and Jódar
, L.
, “Asymptotics of the modified Bessel and the incomplete Gamma matrix functions
,” Appl. Math. Lett.
16
(6
), 815
–820
(2003
).14.
Sastre
, J.
and Defez
, E.
, “On the asymptotics of Laguerre matrix polynomials for large x and n
,” Appl. Math. Lett.
19
(8
), 721
–727
(2006
).15.
Seaborn
, J. B.
, Hypergeometric Functions and Their Applications
(Springer
, New York
, 1991
).16.
Srivastava
, H. M.
, “Hypergeometric functions of three variables
,” Ganita
15
, 97
–108
(1964
).17.
Srivastava
, H. M.
, “Some integrals representing triple hypergeometric functions
,” Rend. Circolo Mat. Palermo
16
(2
), 99
–115
(1967
).18.
Srivastava
, H. M.
and Manocha
, H. L.
, A Treatise on Generating Functions
(John Wiley and Sons
, 1984
).19.
Trefethen
, L. N.
and Embree
, M.
, Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators
(Princeton University Press
, Princeton, NJ
, 2005
).20.
Van Loan
, C.
, “The sensitivity of the matrix exponential
,” SIAM J. Numer. Anal.
14
(6
), 971
–981
(1977
).© 2018 Author(s).
2018
Author(s)
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