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http://dx.doi.org/10.14403/jcms.2011.24.4.12

DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR SOME EXTON HYPERGEOMETRIC FUNCTIONS  

Choi, Junesang (Department of Mathematics Dongguk University)
Hasanov, Anvar (Department of Mathematics Dongguk University)
Turaev, Mamasali (Department of Mathematics Dongguk University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.24, no.4, 2011 , pp. 745-758 More about this Journal
Abstract
Generalizing the Burchnall-Chaundy operator method, the authors are aiming at presenting certain decomposition formulas for the chosen six Exton functions expressed in terms of Appell's functions $F_3$ and $F_4$, Horn's functions $H_3$ and $H_4$, and Gauss's hypergeometric function F. We also give some integral representations for the Exton functions $X_i$ (i = 6, 8, 14) each of whose kernels contains the Horn's function $H_4$.
Keywords
multiple hypergeometric functions; inverse pairs of symbolic operators; generalized inverse pairs of symbolic operators; Exton hypergeometric functions; Horn and Gauss hypergeometric functions; Euler type integrals; integral representations; Mellin-Barnes integrals;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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1 P. Appell and J. Kampe de Feriet, Fonctions Hypergeometriques et Hyper- spheriques; Polynomes d'Hermite, Gauthier - Villars, Paris, 1926.
2 J. L. Burchnall and T. W. Chaundy, Expansions of Appell's double hypergeometric functions, Quart. J. Math. Oxford Ser. 11 (1940), 249-270.   DOI
3 J. L. Burchnall and T. W. Chaundy, Expansions of Appell's double hypergeometric functions. II, Quart. J. Math. Oxford Ser. 12 (1941), 112-128.   DOI
4 T. W. Chaundy, Expansions of hypergeometric functions, Quart. J. Math. Oxford Ser. 13 (1942), 159-171.   DOI
5 J. Choi and A. Hasanov, Applications of the operator H$({\alpha},{\beta})$ to the Humbert double hypergeometric functions, Comput. Math. Appl. 61 (2011), 663-671.   DOI   ScienceOn
6 J. Choi, A. K. Rathie and H. Harsh, Remarks on a summation formula for three variables hypergeometric function and certain hypergeometric transformations, East Asian Math. J. 25 (4) (2009), 481-486.
7 Y. S. Kim and A. K. Rathie, On extension formulas for the triple hypergeometric series due to Exton, Bull. Korean Math. Soc. 44 (2007), no. 4, 743-751.   DOI   ScienceOn
8 Y. S. Kim and A. K. Rathie, Another method for Padmanabham's transforma- tion formula for Exton's triple hypergeometric series, Commun. Korean Math. Soc. 24 (2009), no. 4, 517-521.   DOI   ScienceOn
9 S. W. Lee and Y. S. Kim, An extension of the triple hypergeometric series by Exton, Honam Math. J. 32 (2010), no. 1, 61-71.   DOI   ScienceOn
10 O. I. Marichev, Handbook of Integral Transforms of Higher Transcendental Functions: Theory and algorithmic Tables, Halsted Press (Ellis Horwood Lim- ited, Chichester), Wiley, New York, Chichester, Brisbane and Toronto, 1982.
11 E. G. Poole, Introduction to the Theory of Linear Differential Equations, Clarendon (Oxford University Press), Oxford, 1936.
12 M. S. Salakhitdinov and A. Hasanov, A solution of the Neumann- Dirichlet boundary value problem for generalized bi-axially symmetric Helmholtz equation, Complex Variables and Elliptic Equations 53 (2008), no. 4, 355-364.   DOI   ScienceOn
13 H. M. Srivastava, Hypergeometric functions of three variables, Ganita 15 (1964), 97-108.
14 H. M. Srivastava, Some integrals representing triple hypergeometric functions, Rend. Circ. Mat. Palermo Ser. 2 16 (1967), 99-115.   DOI   ScienceOn
15 H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), Wiley, New York, Chichester, Brisbane, and Toronto, 1985.
16 A. Hasanov and E. T. Karimov, Fundamental solutions for a class of three-dimensional elliptic equations with singular coefficients, Appl. Math. Lett. 22 (2009), 1828-1832.   DOI   ScienceOn
17 A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, Vol. I, McGraw-Hill Book Company, New York, Toronto and London, 1953.
18 H. Exton, Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113-119.
19 A. Hasanov, Fundamental solutions of generalized bi-axially symmetric Helmholtz equation, Complex Variables and Elliptic Equations 52 (2007), no. 8, 673-683.   DOI   ScienceOn
20 A. Hasanov and H. M. Srivastava, Decomposition formulas associated with the Lauricella multivariable hypergeometric functions, Comput. Math. Appl. 53 (2007), 1119-1128.   DOI   ScienceOn
21 A. Hasanov and H. M. Srivastava, Some decomposition formulas associated with the Lauricella function $F^{(r)}_A$ and other multiple hypergeometric functions, Appl. Math. Lett. 19 (2006), 113-121.   DOI   ScienceOn
22 A. Hasanov, H. M. Srivastava, and M. Turaev, Decomposition formulas for some triple hypergeometric functions, J. Math. Anal. Appl. 324 (2006), 955- 969.   DOI   ScienceOn
23 A. Hasanov and M. Turaev, Decomposition formulas for the double hypergeometric functions $G_{1}$ and $G_{2}$, Appl. Math. Comput. 187 (2007), 195-201.   DOI   ScienceOn
24 E. T. Karimov, On a boundary problem with Neumann's condition for 3D singular elliptic equations, Appl. Math. Lett. 23 (2010), 517-522.   DOI   ScienceOn
25 Y. S. Kim, J. Choi and A. K. Rathie, Remark on two results by Padmanabham for Exton's triple hypergeometric series, Honam Math. J. 27 (2005), no. 4, 603- 608.