ON THE GENERATING FUNCTIONS OF THE NEWLY DEFINED GENERALIZED HYPERGEOMETRIC FUNCTIONS

ON THE GENERATING FUNCTIONS OF THE NEWLY DEFINED GENERALIZED HYPERGEOMETRIC FUNCTIONS

E. ATA, İ. O. KIYMAZ

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Abstract. In this paper, we have defined new generalizations of some hypergeometric functions and fractional operators with the help of Fox-Wright function. Then, using each of the generalized fractional operators, we derived linear and bilinear generating function relations for these functions. Finally, we have shown that the newly defined hypergeometric functions and fractional operators can be reduced to functions and operators presented in many studies in the literature by giving special values for their parameters.

Keywords: Beta function, Fox-Wright function, hypergeometric functions, fractional operators, generating functions.

AMS Subject Classification: 33B15, 33C05, 33C65, 26A33, 05A15.