1 |
P. Appell, Sur les fonctions hypergeometriques de plusieurs variables, Memoire Sci. Math. Gauthier-Villars, Paris, 1925.
|
2 |
P. Appell and J. Kampe de Feriet, fonctions hypergeometriques et hyperspheriques, Polynomes d'Hermite. Gauthier-Villars, Paris, 1926.
|
3 |
S. Gaboury and A. K. Rathie, Further hypergeometric identities deducible by fractional calculus, Commun. Korean Math. Soc. 29 (2014), no. 3, 429-437.
DOI
|
4 |
S. Gaboury and R. Tremblay, Remark on certain transformations for multiple hypergeometric functions, Adv. Difference Equ. 2014 (2014), 126, 12 pp.
DOI
|
5 |
A. Hasanov and M. Turaev, Decomposition formulas for the double hypergeometric functions and , Appl. Math. Comput. 187 (2007), no. 1, 195-201.
DOI
|
6 |
Y. S. Kim, J. Choi, and A. K. Rathie, Two results for the terminating (2) with applications, Bull. Korean Math. Soc. 49 (2012), no. 3, 621-633.
DOI
|
7 |
A. R. Miller, A summation formula for Clausen's series (1) with an application to Goursat's function (x), J. Phys. A 38 (2005), no. 16, 3541-3545.
DOI
|
8 |
A. R. Miller and K. S. Ross, An Introduction of the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
|
9 |
T. J. Osler, The fractional derivative of a composite function, SIAM J. Math. Anal. 1 (1970), 288-293.
DOI
|
10 |
R. B. Paris, A Kummer-type transformation for a hypergeometric function, J. Comput. Appl. Math. 173 (2005), no. 2, 379-382.
DOI
|
11 |
E. D. Rainville, Special Functions, The Macmillan Co., New York, 1960.
|
12 |
H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester, 1984.
|
13 |
A. K. Rathie and T. K. Pogany, New summation formula for and a Kummer- type II transformation of (x), Math. Commun. 13 (2008), no. 1, 63-66.
|
14 |
M. Riesz, L'integrale de Riemann-Liouville et le probleme de Cauchy, Acta Math. 81 (1949), 1-223.
DOI
|
15 |
L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, 1966.
|
16 |
H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, Inc., Amsterdam, 2012.
|
17 |
H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester, 1985.
|
18 |
H. M. Srivastava and R. Panda, Some hypergeometric transformations involving Horn's function , Rend. Mat. (6) 6 (1973), 859-864.
|
19 |
H. M. Srivastava and R. Panda, An integral representation for the product of two Jacobi polynomials, J. London Math. Soc. (2) 12 (1975/76), no. 4, 419-425.
|
20 |
R. Tremblay, Une contribution a la theorie de la derive frationnaire, Ph.D. thesis., Laval University, Canada, 1974.
|
21 |
R. Tremblay, S. Gaboury, and B.-J. Fugere, A new transformation formula for fractional derivatives with applications, Integral Transforms Spec. Funct. 24 (2013), no. 3, 172- 186.
DOI
|
22 |
R. Vidunas, Specialization of Appell's functions to univariate hypergeometric functions, J. Math. Anal. Appl. 355 (2009), no. 1, 145-163.
DOI
|
23 |
C. Wei, X. Wang, and Y. Li, Certain transformations for multiple hypergeometric functions, Adv. Difference Equ. 360 (2013), 1-13.
|