Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31532
Operational Representation of Certain Hypergeometric Functions by Means of Fractional Derivatives and Integrals

Authors: Manoj Singh, Mumtaz Ahmad Khan, Abdul Hakim Khan

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1099376

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1174

References:


[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.