{"title":"Operational Representation of Certain Hypergeometric Functions by Means of Fractional Derivatives and Integrals","authors":"Manoj Singh, Mumtaz Ahmad Khan, Abdul Hakim Khan","volume":94,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1375,"pagesEnd":1381,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10000576","abstract":"<p>The investigation in the present paper is to obtain<br \/>\r\ncertain types of relations for the well known hypergeometric functions<br \/>\r\nby employing the technique of fractional derivative and integral.<\/p>\r\n","references":"[1] G. Lauricella, Sulle funzioni ipergeometriche a piu variabili, Rend. Circ.\r\nMat. Palermo, 111-158, 1893.\r\n[2] H. Exton, Multiple Hypergeometric Functions and Applications, Halsted\r\nPress (Ellis Harwood Ltd.) Chichester, 1976.\r\n[3] H. M. Srivastava and P.W. Karlsson, Multiple Gaussian hypergeometric\r\nseries, Halsted press (Ellis Horwood Limited, Chichester), John Wiley\r\nand Sons, New York, Chichester, 1985.\r\n[4] H.M. Srivastava, Generalized Neumann expansion involving\r\nhypergeometric functions, Proc. Camb. Phil. Soc., 63, 425-429,\r\n1967.\r\n[5] M.A. Khan and G.S. Abukhammash, On a generalization of Appell\u2019s\r\nfunctions of two variables, Pro. Mathematica, Vol. XVI, Nos. 31-32,\r\n61-83, 2002.\r\n[6] P. Appell and J. Kamp\u00b4e de F\u00b4eriet, Fonctions hyp\u00b4ergeom\u00b4etriques et\r\nhyperspheriques, Polyn\u02c6omes d\u2019 Hermite Gauthier-Villars, Paris, 1926.\r\n[7] R.C. Pandey, On certain hypergeometric transformations, J. Math. Mech.\r\n12, 113-118, 1963.\r\n[8] S. Saran, Hypergeometric functions of three variables, Ganita, India,\r\nVol.1, No.5, 83-90, 1954.\r\n[9] S.F. Lacroix, Trait\u00b4e du calculus differentiel calcul integral: Mme,\r\nveconrcier, Tome Troisieme, seconde edition, 404-410, 1819.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 94, 2014"}