References
- P. Appell and J. Kampe de Feriet, Fonctions Hypergeometriques et Hyper- spheriques; Polynomes d'Hermite, Gauthier - Villars, Paris, 1926.
- J. L. Burchnall and T. W. Chaundy, Expansions of Appell's double hypergeometric functions, Quart. J. Math. Oxford Ser. 11 (1940), 249-270. https://doi.org/10.1093/qmath/os-11.1.249
- J. L. Burchnall and T. W. Chaundy, Expansions of Appell's double hypergeometric functions. II, Quart. J. Math. Oxford Ser. 12 (1941), 112-128. https://doi.org/10.1093/qmath/os-12.1.112
- T. W. Chaundy, Expansions of hypergeometric functions, Quart. J. Math. Oxford Ser. 13 (1942), 159-171. https://doi.org/10.1093/qmath/os-13.1.159
-
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. https://doi.org/10.1016/j.camwa.2010.12.012 - 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.
- 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.
- H. Exton, Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113-119.
- A. Hasanov, Fundamental solutions of generalized bi-axially symmetric Helmholtz equation, Complex Variables and Elliptic Equations 52 (2007), no. 8, 673-683. https://doi.org/10.1080/17476930701300375
- 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. https://doi.org/10.1016/j.aml.2009.07.006
- A. Hasanov and H. M. Srivastava, Decomposition formulas associated with the Lauricella multivariable hypergeometric functions, Comput. Math. Appl. 53 (2007), 1119-1128. https://doi.org/10.1016/j.camwa.2006.07.007
-
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. https://doi.org/10.1016/j.aml.2005.03.009 - A. Hasanov, H. M. Srivastava, and M. Turaev, Decomposition formulas for some triple hypergeometric functions, J. Math. Anal. Appl. 324 (2006), 955- 969. https://doi.org/10.1016/j.jmaa.2006.01.006
-
A. Hasanov and M. Turaev, Decomposition formulas for the double hypergeometric functions
$G_{1}$ and$G_{2}$ , Appl. Math. Comput. 187 (2007), 195-201. https://doi.org/10.1016/j.amc.2006.08.115 - E. T. Karimov, On a boundary problem with Neumann's condition for 3D singular elliptic equations, Appl. Math. Lett. 23 (2010), 517-522. https://doi.org/10.1016/j.aml.2010.01.002
- 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.
- 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. https://doi.org/10.4134/BKMS.2007.44.4.743
- 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. https://doi.org/10.4134/CKMS.2009.24.4.517
- 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. https://doi.org/10.5831/HMJ.2010.32.1.061
- 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.
- E. G. Poole, Introduction to the Theory of Linear Differential Equations, Clarendon (Oxford University Press), Oxford, 1936.
- 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. https://doi.org/10.1080/17476930701769041
- H. M. Srivastava, Hypergeometric functions of three variables, Ganita 15 (1964), 97-108.
- H. M. Srivastava, Some integrals representing triple hypergeometric functions, Rend. Circ. Mat. Palermo Ser. 2 16 (1967), 99-115. https://doi.org/10.1007/BF02844089
- 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.