Operational Representation of Certain Hypergeometric Functions by Means of Fractional Derivatives and Integrals
The investigation in the present paper is to obtain
certain types of relations for the well known hypergeometric functions
by employing the technique of fractional derivative and integral.
[1] G. Lauricella, Sulle funzioni ipergeometriche a piu variabili, Rend. Circ.
Mat. Palermo, 111-158, 1893.
[2] H. Exton, Multiple Hypergeometric Functions and Applications, Halsted
Press (Ellis Harwood Ltd.) Chichester, 1976.
[3] H. M. Srivastava and P.W. Karlsson, Multiple Gaussian hypergeometric
series, Halsted press (Ellis Horwood Limited, Chichester), John Wiley
and Sons, New York, Chichester, 1985.
[4] H.M. Srivastava, Generalized Neumann expansion involving
hypergeometric functions, Proc. Camb. Phil. Soc., 63, 425-429,
1967.
[5] M.A. Khan and G.S. Abukhammash, On a generalization of Appell’s
functions of two variables, Pro. Mathematica, Vol. XVI, Nos. 31-32,
61-83, 2002.
[6] P. Appell and J. Kamp´e de F´eriet, Fonctions hyp´ergeom´etriques et
hyperspheriques, Polynˆomes d’ Hermite Gauthier-Villars, Paris, 1926.
[7] R.C. Pandey, On certain hypergeometric transformations, J. Math. Mech.
12, 113-118, 1963.
[8] S. Saran, Hypergeometric functions of three variables, Ganita, India,
Vol.1, No.5, 83-90, 1954.
[9] S.F. Lacroix, Trait´e du calculus differentiel calcul integral: Mme,
veconrcier, Tome Troisieme, seconde edition, 404-410, 1819.
[1] G. Lauricella, Sulle funzioni ipergeometriche a piu variabili, Rend. Circ.
Mat. Palermo, 111-158, 1893.
[2] H. Exton, Multiple Hypergeometric Functions and Applications, Halsted
Press (Ellis Harwood Ltd.) Chichester, 1976.
[3] H. M. Srivastava and P.W. Karlsson, Multiple Gaussian hypergeometric
series, Halsted press (Ellis Horwood Limited, Chichester), John Wiley
and Sons, New York, Chichester, 1985.
[4] H.M. Srivastava, Generalized Neumann expansion involving
hypergeometric functions, Proc. Camb. Phil. Soc., 63, 425-429,
1967.
[5] M.A. Khan and G.S. Abukhammash, On a generalization of Appell’s
functions of two variables, Pro. Mathematica, Vol. XVI, Nos. 31-32,
61-83, 2002.
[6] P. Appell and J. Kamp´e de F´eriet, Fonctions hyp´ergeom´etriques et
hyperspheriques, Polynˆomes d’ Hermite Gauthier-Villars, Paris, 1926.
[7] R.C. Pandey, On certain hypergeometric transformations, J. Math. Mech.
12, 113-118, 1963.
[8] S. Saran, Hypergeometric functions of three variables, Ganita, India,
Vol.1, No.5, 83-90, 1954.
[9] S.F. Lacroix, Trait´e du calculus differentiel calcul integral: Mme,
veconrcier, Tome Troisieme, seconde edition, 404-410, 1819.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:69109", author = "Manoj Singh and Mumtaz Ahmad Khan and Abdul Hakim Khan", title = "Operational Representation of Certain Hypergeometric Functions by Means of Fractional Derivatives and Integrals", abstract = "The investigation in the present paper is to obtain
certain types of relations for the well known hypergeometric functions
by employing the technique of fractional derivative and integral.
", keywords = "Fractional Derivatives and Integrals, Hypergeometric
functions. ", volume = "8", number = "10", pages = "1375-6", }